Extrapolation algorithms and Padé approximations: a historical survey

In numerical analysis there are many methods producing sequences. Such is the case of iterative methods, of methods involving series expansions, of discretization methods, that is methods depending on a parameter such that the approximate solution tends to the exact one when the parameter tends to z...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Applied numerical mathematics Ročník 20; číslo 3; s. 299 - 318
Hlavný autor: Brezinski, C.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.03.1996
ISSN:0168-9274, 1873-5460
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract In numerical analysis there are many methods producing sequences. Such is the case of iterative methods, of methods involving series expansions, of discretization methods, that is methods depending on a parameter such that the approximate solution tends to the exact one when the parameter tends to zero, of perturbation methods, etc. Sometimes, the convergence of these sequences is so slow that their effective use is quite limited. The aim of extrapolation methods is to construct a new sequence converging to the same limit faster than the initial one. Among these methods, the most well known are certainly Richardson's extrapolation algorithm and Aitken's gD 2 process. In many branches of applied sciences, the solution of a given problem is often obtained as a power series expansion. The question is then trying to approximate the function from its series expansion. A possible answer is to construct a rational function whose series expansion matches the original one as far as possible. Such rational functions are called Padé approximants. These two subjects, which have some connections, go quite deep and far into the history of mathematics. They are related to continued fractions (a field which goes back to the Greek antiquity), orthogonal polynomials, the moment problem, etc., they played an important role in the development of mathematics (such as the transcendence of e and π) and they have many applications. This paper will give a short historical overview of these two subjects. Of course, we do not pretend to be exhaustive nor even to quote every important contribution. We refer the interested reader to the literature and, in particular, to the recent books [5,22,29,24,38,46,48,68,78,131]. For an extensive bibliography, see [23].
AbstractList In numerical analysis there are many methods producing sequences. Such is the case of iterative methods, of methods involving series expansions, of discretization methods, that is methods depending on a parameter such that the approximate solution tends to the exact one when the parameter tends to zero, of perturbation methods, etc. Sometimes, the convergence of these sequences is so slow that their effective use is quite limited. The aim of extrapolation methods is to construct a new sequence converging to the same limit faster than the initial one. Among these methods, the most well known are certainly Richardson's extrapolation algorithm and Aitken's gD 2 process. In many branches of applied sciences, the solution of a given problem is often obtained as a power series expansion. The question is then trying to approximate the function from its series expansion. A possible answer is to construct a rational function whose series expansion matches the original one as far as possible. Such rational functions are called Padé approximants. These two subjects, which have some connections, go quite deep and far into the history of mathematics. They are related to continued fractions (a field which goes back to the Greek antiquity), orthogonal polynomials, the moment problem, etc., they played an important role in the development of mathematics (such as the transcendence of e and π) and they have many applications. This paper will give a short historical overview of these two subjects. Of course, we do not pretend to be exhaustive nor even to quote every important contribution. We refer the interested reader to the literature and, in particular, to the recent books [5,22,29,24,38,46,48,68,78,131]. For an extensive bibliography, see [23].
Author Brezinski, C.
Author_xml – sequence: 1
  givenname: C.
  surname: Brezinski
  fullname: Brezinski, C.
  email: brezinsk@omega.univ-lille1.fr
  organization: Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq cedex, France
BookMark eNqFkLFOwzAQhi1UJNrCGzBkhCFwdpw47oCEqhaQKsEAs3V1LtQoTSo7VO0j8Ry8GGmLGBhgON3y_af7_gHr1U1NjJ1zuOLAs-tu8lgLJS90egnAOcTqiPV5rpI4lRn0WP8HOWGDEN4AIE0l9Nl0smk9rpoKW9fUEVavjXftYhkirIvoCYvPjwhXK99s3HKPhFGE0cKFtuMsVlF492vanrLjEqtAZ997yF6mk-fxfTx7vHsY385imyhoY56UJaFAKTNETrLgCGpO1pJEyLVWuRBJSsSLuc4ymXW0tlAoIYRWwqbJkI0Od61vQvBUGuva_V-dhasMB7NrxOx0zU7X6NTsGzGqC8tf4ZXvrPz2v9jNIUad2NqRN8E6qi0VzpNtTdG4vw98AV7me6g
CitedBy_id crossref_primary_10_1016_j_ifacol_2019_06_018
crossref_primary_10_1016_S0898_1221_03_80014_7
crossref_primary_10_1016_j_advwatres_2016_01_004
crossref_primary_10_13182_NSE11_05
crossref_primary_10_1016_S0029_5493_02_00043_2
crossref_primary_10_1016_j_jcp_2015_12_059
crossref_primary_10_1007_s11242_024_02070_3
crossref_primary_10_1016_j_apnum_2020_06_007
crossref_primary_10_1016_S0377_0427_00_00360_5
crossref_primary_10_1103_PhysRevX_11_011058
crossref_primary_10_1007_s11045_019_00631_0
crossref_primary_10_1007_s11075_017_0368_z
crossref_primary_10_1109_TCSI_2021_3139141
crossref_primary_10_1080_00150517_2004_12428426
crossref_primary_10_1088_1402_4896_ad7d43
crossref_primary_10_1016_j_proeng_2017_09_212
crossref_primary_10_1115_1_1596555
crossref_primary_10_1002_nme_5497
crossref_primary_10_1061__ASCE_EM_1943_7889_0002040
crossref_primary_10_1016_j_cma_2013_12_003
crossref_primary_10_1016_j_compstruc_2006_08_020
crossref_primary_10_1016_j_ifacol_2022_07_497
crossref_primary_10_1209_0295_5075_132_11001
crossref_primary_10_1016_j_jsv_2003_10_048
crossref_primary_10_1088_1751_8113_41_42_425207
crossref_primary_10_1109_TIM_2019_2890946
crossref_primary_10_1007_s13160_013_0102_8
crossref_primary_10_1088_1751_8121_ab477b
crossref_primary_10_1007_s00211_013_0549_1
crossref_primary_10_1137_18M1170339
crossref_primary_10_1016_j_apnum_2010_03_002
crossref_primary_10_1016_S0377_0427_00_00363_0
crossref_primary_10_1103_PhysRevLett_126_257001
crossref_primary_10_1007_BF02736228
crossref_primary_10_1007_s11075_021_01092_y
crossref_primary_10_1007_s11075_025_02045_5
crossref_primary_10_1137_100808757
crossref_primary_10_1016_j_apnum_2015_03_007
crossref_primary_10_1016_j_jsv_2015_06_039
crossref_primary_10_1016_S0010_4655_98_00111_8
crossref_primary_10_1007_s11075_018_0551_x
crossref_primary_10_1007_s11075_019_00695_w
crossref_primary_10_1093_mnras_stz1792
crossref_primary_10_1016_j_jsv_2006_03_046
crossref_primary_10_1016_j_physa_2023_128610
crossref_primary_10_1038_s44172_025_00343_3
crossref_primary_10_1016_j_talanta_2014_04_067
crossref_primary_10_1016_j_rinam_2025_100549
crossref_primary_10_1016_j_theochem_2007_08_028
crossref_primary_10_1016_S0020_7462_02_00080_X
crossref_primary_10_1140_epjs_s11734_025_01511_4
crossref_primary_10_1016_j_jcp_2020_109835
crossref_primary_10_1016_j_vaccine_2015_05_099
crossref_primary_10_1016_j_ifacol_2022_10_185
crossref_primary_10_1016_j_fluid_2018_11_028
crossref_primary_10_1016_j_ijmecsci_2018_04_058
crossref_primary_10_3390_math12010154
crossref_primary_10_1023_A_1026060404109
crossref_primary_10_1016_j_ifacol_2022_09_052
crossref_primary_10_3390_math13132048
Cites_doi 10.1007/BF01589764
10.1016/0377-0427(95)00157-3
10.1016/0021-9045(76)90044-7
10.1016/0315-0860(84)90002-8
10.1137/0724080
10.2307/3605128
10.1007/BF01930850
10.1051/m2an/197307R100841
10.1007/BF01939615
10.1007/BF02141260
10.1016/0024-3795(93)90220-I
10.1098/rsta.1911.0009
10.1016/0377-0427(87)90182-8
10.1007/s002110050075
10.1007/BF02165234
10.1016/0377-0427(88)90289-0
10.1007/BF02521609
10.1090/S0025-5718-1981-0616372-5
10.1016/0377-0427(91)90095-2
10.1090/S0025-5718-1962-0145647-X
10.1007/BF01399010
10.1016/0377-0427(91)90018-F
10.1103/PhysRev.124.768
10.1007/BF01385877
10.1007/BF02575564
10.1007/BF01389578
10.1016/0168-9274(91)90095-H
10.1007/BF02140685
10.1007/BF02139476
10.1007/BF01939985
10.1093/imanum/3.1.65
10.1016/0168-9274(94)00026-3
10.1137/0720079
10.1098/rsta.1927.0008
10.1007/BF01386416
10.1090/S0025-5718-1972-0314226-X
10.1007/BF01400966
10.1016/0168-9274(85)90036-4
10.1007/BF02575753
10.1080/14786444108520797
10.6028/jres.048.032
10.1007/BF01389488
10.1137/1013092
10.1007/BF02521114
10.5802/afst.108
10.1002/zamm.19610411003
10.1016/0167-7977(89)90011-7
10.1007/BF01396314
10.1007/BF01600331
10.1007/BF01446522
10.1007/BF02142326
10.1002/sapm19553411
10.1007/BF01385628
10.24033/bsmf.653
10.1137/0708037
10.1007/BF02141936
10.1007/BF02279938
10.1007/BF01385846
10.1515/crll.1878.84.242
10.5802/afst.34
ContentType Journal Article
Copyright 1996
Copyright_xml – notice: 1996
DBID AAYXX
CITATION
DOI 10.1016/0168-9274(95)00110-7
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
EISSN 1873-5460
EndPage 318
ExternalDocumentID 10_1016_0168_9274_95_00110_7
0168927495001107
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1RT
1~.
1~5
23M
4.4
457
4G.
5GY
5VS
7-5
71M
8P~
9JN
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
ABAOU
ABEFU
ABJNI
ABMAC
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACRLP
ADBBV
ADEZE
ADGUI
ADIYS
ADMUD
AEBSH
AEKER
AENEX
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AI.
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HMJ
HVGLF
HZ~
IHE
J1W
KOM
M26
M41
MHUIS
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SME
SPC
SPCBC
SSW
SSZ
T5K
TN5
VH1
VOH
WH7
WUQ
XPP
ZMT
~02
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
ID FETCH-LOGICAL-c370t-13ffea2a446aa1e4d1a07becce4a0899782235ee1db96646ffe9c0d7222972c53
ISICitedReferencesCount 77
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=0168927495001107&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0168-9274
IngestDate Sat Nov 29 02:29:37 EST 2025
Tue Nov 18 22:35:25 EST 2025
Fri Feb 23 02:29:21 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
License https://www.elsevier.com/tdm/userlicense/1.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c370t-13ffea2a446aa1e4d1a07becce4a0899782235ee1db96646ffe9c0d7222972c53
PageCount 20
ParticipantIDs crossref_citationtrail_10_1016_0168_9274_95_00110_7
crossref_primary_10_1016_0168_9274_95_00110_7
elsevier_sciencedirect_doi_10_1016_0168_9274_95_00110_7
PublicationCentury 1900
PublicationDate 1996-03-01
PublicationDateYYYYMMDD 1996-03-01
PublicationDate_xml – month: 03
  year: 1996
  text: 1996-03-01
  day: 01
PublicationDecade 1990
PublicationTitle Applied numerical mathematics
PublicationYear 1996
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Joyce (BIB69) 1971; 13
Lavastre (BIB74) 1994; 15
Draux (BIB48) 1983; 974
Brezinski (BIB18) 1985; 46
Jones, Thron (BIB68) 1980
Powell, Shah (BIB101) 1972
de Montessus de Ballore (BIB91) 1902; 30
Naegelsbach, Naegelsbach (BIB94) 1876; 59
C. Brezinski and A.C. Matos, A derivation of extrapolation algorithms based on error estimates
Brezinski, Redivo Zaglia (BIB29) 1991
Rutishauser (BIB107) 1954; 5
Sidi (BIB119) 1990; 57
van Assche (BIB124) 1987; 1265
Delahaye, Germain-Bonne (BIB47) 1980; 35
Håvie (BIB60) 1979; 19
Sheppard (BIB117) 1900; 32
Marchuk, Shaidurov (BIB83) 1983
Walz (BIB128) 1991
Bogolyubov, Krylov (BIB10) 1926; 3
Chabert (BIB41) 1994
Stieltjes (BIB123) 1894; 8
Berlinet (BIB9) 1985; 1
Andoyer, Andoyer (BIB3) 1904–1912; vol. 4
Richardson (BIB104) 1910; 210
Benchiboun (BIB8) 1987; I
Brezinski, Redivo Zaglia (BIB28) 1991; 8
A.C. Matos, Linear difference operators and acceleration methods, submitted.
Delahaye (BIB46) 1988
Wynn (BIB133) 1956; 52
Milne (BIB90) 1903; 2
Stiefel (BIB121) 1961; 41
Brezinski (BIB15) 1980; 35
Gekeler (BIB53) 1972; 26
Cuyt, Wuytack (BIB44) 1987
Lubinsky (BIB79) 1988; 202
Moussa (BIB92) 1994
Schneider (BIB114) 1975; 24
McLeod (BIB88) 1971; 7
Baker, Graves-Morris, Baker, Graves-Morris (BIB5) 1981; 2 vols
Schmidt (BIB113) 1941; 7
Pryce (BIB103) 1993
(BIB95) 1990
Bulirsch, Stoer (BIB37) 1966; 8
Rutishauser (BIB108) 1955; 6
Stahl, Totik (BIB120) 1992
Wynn (BIB132) 1956; 10
Rutishauser (BIB109) 1963; 5
to appear.
Jbilou, Sadok (BIB67) 1991; 36
Brezinski, Walz (BIB36) 1991; 34
Salam (BIB112) 1994; 7
Shanks (BIB116) 1955; 34
Stieltjes (BIB122) 1889; 3
Jacobi (BIB66) 1845; 30
Lagrange, Lagrange (BIB71) 1776; 7
Germain-Bonne (BIB55) 1978; I
Brezinski (BIB13) 1971; 273 A
Huygens (BIB65) 1654
Gragg (BIB56) 1965; 2
Brezinski, Redivo Zaglia, Sadok (BIB33) 1992; 63
O'Beirne (BIB97) 1947
Edrei, Saff, Varga (BIB51) 1983; 1002
Romberg (BIB106) 1955; 28
Brezinski, Redivo Zaglia (BIB30) 1994; 7
Dutka (BIB50) 1984; 11
Graves-Morris (BIB57) 1983; 42
Henrici (BIB63) 1958; 49
Hermite, Hermite, Hermite, Hermite (BIB64) 1873; 77
Levin (BIB76) 1973; B3
Brezinski, Rieu (BIB34) 1974; 28
Hankel (BIB62) 1861
Overholt (BIB98) 1965; 5
van Iseghem (BIB127) 1994; 68
Brezinski, Delahaye, Germain-Bonne (BIB26) 1983; 20
Brezinski (BIB21) 1989; 2
Sadok (BIB110) 1993; 190
Brezinski (BIB22) 1990
Cantor (BIB39) 1878; 84
Mühlbach (BIB93) 1976
Bauer (BIB6) 1961
Matos (BIB84) 1990; 58
Draux, van Ingelandt (BIB49) 1987
van Iseghem (BIB125) 1985
Brezinski (BIB14) 1975; 12
Lubkin (BIB81) 1952; 48
Maxwell (BIB87) 1892
Brezinski (BIB17) 1983; 3
Cordellier (BIB43) 1979; 765
Brezinski, van Iseghem (BIB35) 1994; Vol. III
Carstensen (BIB40) 1989
Beckermann (BIB7) 1989
Wynn (BIB135) 1963; 3
Brezinski (BIB12) 1970; 271 A
Lambert (BIB72) 1758; 3
Sidi (BIB118) 1988; 22
van Iseghem (BIB126) 1987; 19
Kommerell (BIB70) 1936
Meinardus, Taylor (BIB89) 1976; 16
Bultheel (BIB38) 1987
Lindemann (BIB77) 1882; 20
Shanks (BIB115) 1949
(BIB1) 1965
Baker (BIB4) 1961; 124
Brezinski (BIB23) 1991
Laurent (BIB73) 1963; 256
Gray, Atchison, McWilliams (BIB58) 1971; 8
Le Ferrand (BIB75) 1992; 3
Germain-Bonne (BIB54) 1973; R1
Brezinski (BIB20) 1988; 86
Gutknecht (BIB59) 1990
Aitken (BIB2) 1926; 46
Prévost (BIB102) 1994; 2
Bolton, Scoins (BIB11) 1956; 52
Delahaye (BIB45) 1981; 37
Lorentzen, Waadeland (BIB78) 1992
Brezinski (BIB19) 1988
Brezinski, Redivo Zaglia, Sadok (BIB32) 1991; 1
Brezinski, Redivo Zaglia (BIB31) 1994; 2
Brezinski (BIB16) 1980; 50
Weniger (BIB130) 1989; 10
Maclaurin (BIB82) 1742
Ford, Sidi (BIB52) 1987; 24
Richardson (BIB105) 1927; 226
Hairer, Wanner (BIB61) 1991
Brezinski (BIB24) 1991
Matos, Prévost (BIB86) 1992; 2
Saigey (BIB111) 1859
Padé (BIB99) 1892; 9
Brezinski (BIB25) 1994; 2
G. Walz
Collatz (BIB42) 1951
Lubinsky, Saff (BIB80) 1988; 1305
Pennacchi (BIB100) 1968; 5
Wynn (BIB134) 1962; 16
Nikishin, Sorokin (BIB96) 1991; 92
Wimp (BIB131) 1981
Draux (10.1016/0168-9274(95)00110-7_BIB48) 1983; 974
Baker (10.1016/0168-9274(95)00110-7_BIB5_2) 1996; 2 vols.
Håvie (10.1016/0168-9274(95)00110-7_BIB60) 1979; 19
Lambert (10.1016/0168-9274(95)00110-7_BIB72) 1758; 3
Richardson (10.1016/0168-9274(95)00110-7_BIB105) 1927; 226
Stahl (10.1016/0168-9274(95)00110-7_BIB120) 1992
Laurent (10.1016/0168-9274(95)00110-7_BIB73) 1963; 256
Sadok (10.1016/0168-9274(95)00110-7_BIB110) 1993; 190
Bauer (10.1016/0168-9274(95)00110-7_BIB6) 1961
Germain-Bonne (10.1016/0168-9274(95)00110-7_BIB54) 1973; R1
Andoyer (10.1016/0168-9274(95)00110-7_BIB3_1) 1904; vol. 4
van Iseghem (10.1016/0168-9274(95)00110-7_BIB127) 1994; 68
Brezinski (10.1016/0168-9274(95)00110-7_BIB34) 1974; 28
Maxwell (10.1016/0168-9274(95)00110-7_BIB87) 1892
Matos (10.1016/0168-9274(95)00110-7_BIB84) 1990; 58
Hairer (10.1016/0168-9274(95)00110-7_BIB61) 1991
Hermite (10.1016/0168-9274(95)00110-7_BIB64_1) 1873; 77
Brezinski (10.1016/0168-9274(95)00110-7_BIB28) 1991; 8
Hankel (10.1016/0168-9274(95)00110-7_BIB62) 1861
Berlinet (10.1016/0168-9274(95)00110-7_BIB9) 1985; 1
Brezinski (10.1016/0168-9274(95)00110-7_BIB19) 1988
Brezinski (10.1016/0168-9274(95)00110-7_BIB32) 1991; 1
Powell (10.1016/0168-9274(95)00110-7_BIB101) 1972
Gekeler (10.1016/0168-9274(95)00110-7_BIB53) 1972; 26
Milne (10.1016/0168-9274(95)00110-7_BIB90) 1903; 2
Rutishauser (10.1016/0168-9274(95)00110-7_BIB108) 1955; 6
Gutknecht (10.1016/0168-9274(95)00110-7_BIB59) 1990
Collatz (10.1016/0168-9274(95)00110-7_BIB42) 1951
Brezinski (10.1016/0168-9274(95)00110-7_BIB20) 1988; 86
Lavastre (10.1016/0168-9274(95)00110-7_BIB74) 1994; 15
Stieltjes (10.1016/0168-9274(95)00110-7_BIB123) 1894; 8
Cantor (10.1016/0168-9274(95)00110-7_BIB39) 1878; 84
Edrei (10.1016/0168-9274(95)00110-7_BIB51) 1983; 1002
Brezinski (10.1016/0168-9274(95)00110-7_BIB21) 1989; 2
Sidi (10.1016/0168-9274(95)00110-7_BIB119) 1990; 57
Jones (10.1016/0168-9274(95)00110-7_BIB68) 1980
Delahaye (10.1016/0168-9274(95)00110-7_BIB46) 1988
Wynn (10.1016/0168-9274(95)00110-7_BIB134) 1962; 16
(10.1016/0168-9274(95)00110-7_BIB99_2) 1984
Baker (10.1016/0168-9274(95)00110-7_BIB5_1) 1981; 2 vols
Delahaye (10.1016/0168-9274(95)00110-7_BIB45) 1981; 37
Ford (10.1016/0168-9274(95)00110-7_BIB52) 1987; 24
Salam (10.1016/0168-9274(95)00110-7_BIB112) 1994; 7
10.1016/0168-9274(95)00110-7_BIB27
Chabert (10.1016/0168-9274(95)00110-7_BIB41) 1994
Cordellier (10.1016/0168-9274(95)00110-7_BIB43) 1979; 765
Kommerell (10.1016/0168-9274(95)00110-7_BIB70) 1936
Andoyer (10.1016/0168-9274(95)00110-7_BIB3_2) 1993; vol. 4
10.1016/0168-9274(95)00110-7_BIB129
Brezinski (10.1016/0168-9274(95)00110-7_BIB26) 1983; 20
Brezinski (10.1016/0168-9274(95)00110-7_BIB30) 1994; 7
Brezinski (10.1016/0168-9274(95)00110-7_BIB35) 1994; Vol. III
Bultheel (10.1016/0168-9274(95)00110-7_BIB38) 1987
Dutka (10.1016/0168-9274(95)00110-7_BIB50) 1984; 11
Lagrange (10.1016/0168-9274(95)00110-7_BIB71_1) 1776; 7
Henrici (10.1016/0168-9274(95)00110-7_BIB63) 1958; 49
Jbilou (10.1016/0168-9274(95)00110-7_BIB67) 1991; 36
(10.1016/0168-9274(95)00110-7_BIB95) 1990
van Iseghem (10.1016/0168-9274(95)00110-7_BIB126) 1987; 19
Jacobi (10.1016/0168-9274(95)00110-7_BIB66) 1845; 30
Bogolyubov (10.1016/0168-9274(95)00110-7_BIB10) 1926; 3
Hermite (10.1016/0168-9274(95)00110-7_BIB64_4) 1873; 77
10.1016/0168-9274(95)00110-7_BIB85
Germain-Bonne (10.1016/0168-9274(95)00110-7_BIB55) 1978; I
Pryce (10.1016/0168-9274(95)00110-7_BIB103) 1993
Wynn (10.1016/0168-9274(95)00110-7_BIB135) 1963; 3
Wimp (10.1016/0168-9274(95)00110-7_BIB131) 1981
Bulirsch (10.1016/0168-9274(95)00110-7_BIB37) 1966; 8
Delahaye (10.1016/0168-9274(95)00110-7_BIB47) 1980; 35
Prévost (10.1016/0168-9274(95)00110-7_BIB102) 1994; 2
Brezinski (10.1016/0168-9274(95)00110-7_BIB13) 1971; 273 A
Nikishin (10.1016/0168-9274(95)00110-7_BIB96) 1991; 92
Saigey (10.1016/0168-9274(95)00110-7_BIB111) 1859
Padé (10.1016/0168-9274(95)00110-7_BIB99_1) 1892; 9
Schmidt (10.1016/0168-9274(95)00110-7_BIB113) 1941; 7
Beckermann (10.1016/0168-9274(95)00110-7_BIB7) 1989
Weniger (10.1016/0168-9274(95)00110-7_BIB130) 1989; 10
(10.1016/0168-9274(95)00110-7_BIB1) 1965
Gragg (10.1016/0168-9274(95)00110-7_BIB56) 1965; 2
Brezinski (10.1016/0168-9274(95)00110-7_BIB15) 1980; 35
Le Ferrand (10.1016/0168-9274(95)00110-7_BIB75) 1992; 3
Shanks (10.1016/0168-9274(95)00110-7_BIB115) 1949
Sidi (10.1016/0168-9274(95)00110-7_BIB118) 1988; 22
Bolton (10.1016/0168-9274(95)00110-7_BIB11) 1956; 52
Hermite (10.1016/0168-9274(95)00110-7_BIB64_3) 1873; 77
Richardson (10.1016/0168-9274(95)00110-7_BIB104) 1910; 210
Aitken (10.1016/0168-9274(95)00110-7_BIB2) 1926; 46
Shanks (10.1016/0168-9274(95)00110-7_BIB116) 1955; 34
Wynn (10.1016/0168-9274(95)00110-7_BIB133) 1956; 52
Lubinsky (10.1016/0168-9274(95)00110-7_BIB79) 1988; 202
Brezinski (10.1016/0168-9274(95)00110-7_BIB24) 1991
Stiefel (10.1016/0168-9274(95)00110-7_BIB121) 1961; 41
Lubinsky (10.1016/0168-9274(95)00110-7_BIB80) 1988; 1305
Lorentzen (10.1016/0168-9274(95)00110-7_BIB78) 1992
Levin (10.1016/0168-9274(95)00110-7_BIB76) 1973; B3
Mühlbach (10.1016/0168-9274(95)00110-7_BIB93) 1976
Naegelsbach (10.1016/0168-9274(95)00110-7_BIB94_1) 1876; 59
Brezinski (10.1016/0168-9274(95)00110-7_BIB18) 1985; 46
Brezinski (10.1016/0168-9274(95)00110-7_BIB16) 1980; 50
Brezinski (10.1016/0168-9274(95)00110-7_BIB17) 1983; 3
Carstensen (10.1016/0168-9274(95)00110-7_BIB40) 1989
Joyce (10.1016/0168-9274(95)00110-7_BIB69) 1971; 13
Schneider (10.1016/0168-9274(95)00110-7_BIB114) 1975; 24
Sheppard (10.1016/0168-9274(95)00110-7_BIB117) 1900; 32
de Montessus de Ballore (10.1016/0168-9274(95)00110-7_BIB91) 1902; 30
van Assche (10.1016/0168-9274(95)00110-7_BIB124) 1987; 1265
Marchuk (10.1016/0168-9274(95)00110-7_BIB83) 1983
Romberg (10.1016/0168-9274(95)00110-7_BIB106) 1955; 28
Brezinski (10.1016/0168-9274(95)00110-7_BIB22) 1990
Lagrange (10.1016/0168-9274(95)00110-7_BIB71_2) 1869; 4
Lubkin (10.1016/0168-9274(95)00110-7_BIB81) 1952; 48
Wynn (10.1016/0168-9274(95)00110-7_BIB132) 1956; 10
Stieltjes (10.1016/0168-9274(95)00110-7_BIB122) 1889; 3
Draux (10.1016/0168-9274(95)00110-7_BIB49) 1987
Cuyt (10.1016/0168-9274(95)00110-7_BIB44) 1987
Pennacchi (10.1016/0168-9274(95)00110-7_BIB100) 1968; 5
Matos (10.1016/0168-9274(95)00110-7_BIB86) 1992; 2
van Iseghem (10.1016/0168-9274(95)00110-7_BIB125) 1985
Brezinski (10.1016/0168-9274(95)00110-7_BIB12) 1970; 271 A
Lindemann (10.1016/0168-9274(95)00110-7_BIB77) 1882; 20
Baker (10.1016/0168-9274(95)00110-7_BIB4) 1961; 124
Benchiboun (10.1016/0168-9274(95)00110-7_BIB8) 1987; I
Huygens (10.1016/0168-9274(95)00110-7_BIB65) 1654
Meinardus (10.1016/0168-9274(95)00110-7_BIB89) 1976; 16
Gray (10.1016/0168-9274(95)00110-7_BIB58) 1971; 8
Brezinski (10.1016/0168-9274(95)00110-7_BIB14) 1975; 12
Brezinski (10.1016/0168-9274(95)00110-7_BIB23) 1991
Brezinski (10.1016/0168-9274(95)00110-7_BIB31) 1994; 2
Brezinski (10.1016/0168-9274(95)00110-7_BIB33) 1992; 63
Overholt (10.1016/0168-9274(95)00110-7_BIB98) 1965; 5
Naegelsbach (10.1016/0168-9274(95)00110-7_BIB94_2) 1877; 61
Hermite (10.1016/0168-9274(95)00110-7_BIB64_2) 1873; 77
Brezinski (10.1016/0168-9274(95)00110-7_BIB36) 1991; 34
O'Beirne (10.1016/0168-9274(95)00110-7_BIB97) 1947
Rutishauser (10.1016/0168-9274(95)00110-7_BIB107) 1954; 5
Rutishauser (10.1016/0168-9274(95)00110-7_BIB109) 1963; 5
Walz (10.1016/0168-9274(95)00110-7_BIB128) 1991
Brezinski (10.1016/0168-9274(95)00110-7_BIB25) 1994; 2
Graves-Morris (10.1016/0168-9274(95)00110-7_BIB57) 1983; 42
McLeod (10.1016/0168-9274(95)00110-7_BIB88) 1971; 7
Brezinski (10.1016/0168-9274(95)00110-7_BIB29) 1991
Maclaurin (10.1016/0168-9274(95)00110-7_BIB82) 1742
Moussa (10.1016/0168-9274(95)00110-7_BIB92) 1994
References_xml – volume: 2
  start-page: 384
  year: 1965
  end-page: 403
  ident: BIB56
  article-title: On extrapolation algorithms for initial-value problems
  publication-title: SIAM J. Numer. Anal.
– volume: 6
  start-page: 387
  year: 1955
  end-page: 401
  ident: BIB108
  article-title: Bestimmung der Eigenwerte und Eigenvektoren einer Matrix mit Hilfe des Quotienten-Differenzen-Algorithmus
  publication-title: Z. Angew. Math. Phys.
– volume: 24
  start-page: 1212
  year: 1987
  end-page: 1232
  ident: BIB52
  article-title: An algorithm for a generalization of the Richardson extrapolation process
  publication-title: SIAM J. Numer. Anal.
– year: 1988
  ident: BIB46
  article-title: Sequence Transformations
– year: 1992
  ident: BIB120
  article-title: General Orthogonal Polynomials
– volume: 3
  start-page: 65
  year: 1983
  end-page: 80
  ident: BIB17
  article-title: Error control in convergence acceleration processes
  publication-title: IMA J. Numer. Anal.
– year: 1983
  ident: BIB83
  article-title: Difference Methods and their Extrapolations
– year: 1980
  ident: BIB68
  article-title: Continued Fractions, Analytic Theory and Applications
– volume: 10
  start-page: 189
  year: 1989
  end-page: 371
  ident: BIB130
  article-title: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
  publication-title: Comput. Physics Reports
– year: 1991
  ident: BIB29
  article-title: Extrapolation Methods. Theory and Practice
– volume: 84
  start-page: 242
  year: 1878
  end-page: 258
  ident: BIB39
  article-title: Ein Beitrag zur Mannigfaltigkeitslehre
  publication-title: J. Reine Angew. Math.
– volume: 2
  start-page: 130
  year: 1994
  end-page: 137
  ident: BIB25
  article-title: The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer
  publication-title: Elect. Trans. Numer. Anal.
– year: 1991
  ident: BIB23
  article-title: A Bibliography on Continued Fractions, Padé Approximation, Extrapolation and Related Subjects
– volume: 32
  start-page: 258
  year: 1900
  end-page: 277
  ident: BIB117
  article-title: Some quadrature formulas
  publication-title: Proc. London Math. Soc.
– year: 1861
  ident: BIB62
  article-title: Ueber eine besondere Classe der symmetrischen Determinanten
  publication-title: Inaugural Diss.
– year: 1965
  ident: BIB1
  publication-title: Handbook of Mathematical Functions
– year: 1987
  ident: BIB49
  article-title: Polynômes Orthogonaux et Approximants de Padé, Logiciels
– volume: 2
  start-page: 309
  year: 1903
  end-page: 311
  ident: BIB90
  article-title: Extension of Huygen's approximation to a circular arc
  publication-title: Math. Gaz.
– year: 1987
  ident: BIB38
  article-title: Laurent Series and their Padé Approximations
– volume: B3
  start-page: 371
  year: 1973
  end-page: 388
  ident: BIB76
  article-title: Development of nonlinear transformations for improving convergence of sequences
  publication-title: Int. J. Comput. Math.
– volume: 68
  start-page: 549
  year: 1994
  end-page: 562
  ident: BIB127
  article-title: Convergence of vectorial sequences. Applications
  publication-title: Numer. Math.
– volume: 41
  start-page: 408
  year: 1961
  end-page: 413
  ident: BIB121
  article-title: Altes und neues über numerische Quadratur
  publication-title: Z. Angew. Math. Mech.
– year: 1993
  ident: BIB103
  article-title: Numerical Solution of Sturm-Liouville Problems
– year: 1972
  ident: BIB101
  article-title: Summability Theory and its Applications
– volume: 124
  start-page: 768
  year: 1961
  end-page: 774
  ident: BIB4
  article-title: Application of the Padé method to the investigation of some magnetic properties of the Ising model
  publication-title: Phys. Rev.
– volume: 19
  start-page: 141
  year: 1987
  end-page: 150
  ident: BIB126
  article-title: Vector orthogonal relations. Vector QD algorithm
  publication-title: J. Comput. Appl. Math.
– volume: 50
  year: 1980
  ident: BIB16
  article-title: Padé-Type Approximation and General Orthogonal Polynomials
  publication-title: ISNM
– volume: 58
  start-page: 329
  year: 1990
  end-page: 340
  ident: BIB84
  article-title: Acceleration methods based on convergence tests
  publication-title: Numer. Math.
– volume: 2
  start-page: 461
  year: 1994
  end-page: 477
  ident: BIB31
  article-title: A general extrapolation procedure revisited
  publication-title: Adv. Comput. Math.
– volume: 3
  start-page: 273
  year: 1992
  end-page: 284
  ident: BIB75
  article-title: Convergence of the topological ϵ-algorithm for solving systems of nonlinear equations
  publication-title: Numerical Algor.
– start-page: 443
  year: 1989
  end-page: 446
  ident: BIB7
  article-title: A connection between the
  publication-title: Numerical and Applied Mathematics
– volume: 974
  year: 1983
  ident: BIB48
  article-title: Polynômes Orthogonaux Formels. Applications
  publication-title: Lecture Notes in Mathematics
– start-page: 200
  year: 1976
  end-page: 212
  ident: BIB93
  article-title: Neville-Aitken algorithms for interpolating by functions of Čebyšev-systems in the sense of Newton and in a generalized sense of Hermite
  publication-title: Theory of Approximation with Applications
– volume: 35
  start-page: 175
  year: 1980
  end-page: 187
  ident: BIB15
  article-title: A general extrapolation algorithm
  publication-title: Numer. Math.
– volume: I
  year: 1978
  ident: BIB55
  article-title: Estimation de la Limite de Suites et Formalisation de Procédés d'Accélération de la Convergence
  publication-title: Thèse d'Etat
– volume: 15
  start-page: 77
  year: 1994
  end-page: 98
  ident: BIB74
  article-title: On the stochastic acceleration of sequences of random variables
  publication-title: Appl. Numer. Math.
– volume: 19
  start-page: 204
  year: 1979
  end-page: 213
  ident: BIB60
  article-title: Generalized Neville type extrapolation schemes
  publication-title: BIT
– volume: 202
  year: 1988
  ident: BIB79
  article-title: Strong Asymptotics for Extremal Errors and Polynomials Associated with Erdõs-type Weights
  publication-title: Pitman Research Notes
– volume: vol. 4
  start-page: 127
  year: 1904–1912
  end-page: 160
  ident: BIB3
  article-title: Interpolation
  publication-title: Encyclopédie des Sciences Mathématiques Pures et Appliquées
– year: 1947
  ident: BIB97
  article-title: On linear iterative processes and on methods of improving the convergence of certain types of iterated sequences
– volume: 26
  start-page: 427
  year: 1972
  end-page: 436
  ident: BIB53
  article-title: On the solution of systems of equations by the epsilon algorithm of Wynn
  publication-title: Math. Comp.
– year: 1981
  ident: BIB131
  article-title: Sequence Transformations and their Applications
– volume: 2
  start-page: 393
  year: 1992
  end-page: 408
  ident: BIB86
  article-title: Acceleration property for the columns of the
  publication-title: Numerical Algor.
– volume: 8
  start-page: 1
  year: 1894
  end-page: 122
  ident: BIB123
  article-title: Recherches sur les fractions continues
  publication-title: Ann. Fac. Sci. Toulouse
– volume: 3
  start-page: 3
  year: 1926
  end-page: 22
  ident: BIB10
  article-title: On Rayleigh's principle in the theory of differential equations of mathematical physics and upon Euler's method in the calculus of variation
  publication-title: Acad. Sci. Ukraine (Phys. Math.)
– volume: 52
  start-page: 215
  year: 1956
  end-page: 229
  ident: BIB11
  article-title: Eigenvalues of differential equations by finite-difference methods
  publication-title: Proc. Cambridge Phil. Soc.
– volume: 3
  start-page: 128
  year: 1758
  end-page: 168
  ident: BIB72
  article-title: Observationes variae in mathesin puram
  publication-title: Acta Helvetica
– volume: 190
  start-page: 71
  year: 1993
  end-page: 85
  ident: BIB110
  article-title: Quasilinear vector extrapolation methods
  publication-title: Linear Alg. Appl.
– year: 1990
  ident: BIB95
  publication-title: Orthogonal Polynomials: Theory and Practice
– start-page: 73
  year: 1985
  end-page: 77
  ident: BIB125
  article-title: Vector Padé approximants
  publication-title: Numerical Mathematics and Applications
– year: 1859
  ident: BIB111
  article-title: Problèmes d'Arithmétique et Exercices de Calcul du Second Degré avec les Solutions Raisonnées
– volume: 273 A
  start-page: 727
  year: 1971
  end-page: 730
  ident: BIB13
  article-title: Accélération de suites à convergence logarithmique
  publication-title: C. R. Acad. Sci. Paris
– volume: 5
  start-page: 48
  year: 1963
  end-page: 54
  ident: BIB109
  article-title: Ausdehnung des Rombergschen Prinzips
  publication-title: Numer. Math.
– volume: 49
  start-page: 23
  year: 1958
  end-page: 46
  ident: BIB63
  article-title: The quotient-difference algorithm
  publication-title: Nat. Bur. Stand. Appl. Math. Ser.
– volume: 20
  start-page: 213
  year: 1882
  end-page: 225
  ident: BIB77
  article-title: Ueber die Zahl π
  publication-title: Math. Ann.
– year: 1990
  ident: BIB22
  article-title: History of Continued Fractions and Padé Approximants
– volume: 1305
  year: 1988
  ident: BIB80
  article-title: Strong Asymptotics for Extremal Polynomials Associated with Weights on
  publication-title: Lecture Notes in Mathematics
– volume: 1265
  year: 1987
  ident: BIB124
  article-title: Asymptotics for Orthogonal Polynomials
  publication-title: Lecture Notes in Mathematics
– volume: R1
  start-page: 84
  year: 1973
  end-page: 90
  ident: BIB54
  article-title: Transformations de suites
  publication-title: RAIRO
– volume: 2 vols
  year: 1981
  ident: BIB5
  publication-title: Padé Approximants
– year: 1991
  ident: BIB24
  article-title: Biorthogonality and its Applications to Numerical Analysis
– year: 1949
  ident: BIB115
  article-title: An analogy between transient and mathematical sequences and some nonlinear sequence-to-sequence transforms suggested by it, Part I, Memorandum 9994,
– volume: 48
  start-page: 228
  year: 1952
  end-page: 254
  ident: BIB81
  article-title: A method of summing infinite series
  publication-title: J. Res. Nat. Bur. Stand.
– volume: 5
  start-page: 233
  year: 1954
  end-page: 251
  ident: BIB107
  article-title: Der Quotienten-Differenzen-Algorithmus
  publication-title: Z. Angew. Math. Phys.
– volume: 42
  start-page: 331
  year: 1983
  end-page: 348
  ident: BIB57
  article-title: Vector valued rational interpolants I
  publication-title: Numer. Math.
– volume: 57
  start-page: 365
  year: 1990
  end-page: 377
  ident: BIB119
  article-title: On a generalization of the Richardson extrapolation process
  publication-title: Numer. Math.
– volume: 271 A
  start-page: 1174
  year: 1970
  end-page: 1177
  ident: BIB12
  article-title: Application de l'ϵ-algorithme à la résoltion des systèmes non linéaires
  publication-title: C. R. Acad. Sci. Paris
– volume: 59
  start-page: 147
  year: 1876
  end-page: 192
  ident: BIB94
  article-title: Studien zu Fürstenau's neuer Methode der Darstellung und Berechnung der Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten
  publication-title: Arch. Math. Phys.
– year: 1892
  ident: BIB87
  article-title: A Treatise on Electricity and Magnetism
– volume: 1
  start-page: 261
  year: 1991
  end-page: 274
  ident: BIB32
  article-title: Avoiding breakdown and near-breakdown in Lanczos type algorithms
  publication-title: Numerical Algor.
– volume: 3
  start-page: H.1
  year: 1889
  end-page: 17
  ident: BIB122
  article-title: Sur la réduction en fraction continue d'une série procédant suivant les puissances descendantes d'une variable
  publication-title: Ann. Fac. Sci. Toulouse
– year: 1990
  ident: BIB59
  article-title: The unsymmetric Lanczos algorithms and their relations to Padé approximation, continued fractions, and the
  publication-title: Proceedings of the Copper Mountain Conference on Iterative Methods
– volume: 7
  start-page: 17
  year: 1971
  end-page: 24
  ident: BIB88
  article-title: A note on the ϵ-algorithm
  publication-title: Computing
– volume: 8
  start-page: 365
  year: 1971
  end-page: 381
  ident: BIB58
  article-title: Higher order
  publication-title: SIAM J. Numer. Anal.
– volume: 63
  start-page: 29
  year: 1992
  end-page: 38
  ident: BIB33
  article-title: A breakdown-free Lanczos type algorithm for solving linear systems
  publication-title: Numer. Math.
– volume: Vol. III
  start-page: 47
  year: 1994
  end-page: 222
  ident: BIB35
  article-title: Padé approximations
  publication-title: Handbook of Numerical Analysis
– volume: 1002
  year: 1983
  ident: BIB51
  article-title: Zeros of Sections of Power Series
  publication-title: Lecture Notes in Mathematics
– year: 1991
  ident: BIB128
  article-title: The history of extrapolation methods in numerical analysis
  publication-title: Report No. 130
– volume: 46
  start-page: 311
  year: 1985
  end-page: 321
  ident: BIB18
  article-title: Composite sequence transformations
  publication-title: Numer. Math.
– volume: 86
  start-page: 61
  year: 1988
  end-page: 78
  ident: BIB20
  article-title: Quasi-linear extrapolation processes
  publication-title: Numerical Mathematics Singapore 1988
– volume: 30
  start-page: 127
  year: 1845
  end-page: 156
  ident: BIB66
  article-title: Über die Darstellung einer Reihe gegebener Werthe durch eine gebrochen rationale Funktion
  publication-title: J. Reine Angew. Math.
– reference: A.C. Matos, Linear difference operators and acceleration methods, submitted.
– volume: 16
  start-page: 301
  year: 1962
  end-page: 322
  ident: BIB134
  article-title: Acceleration techniques for iterated vector and matrix problems
  publication-title: Math. Comp.
– start-page: 373
  year: 1988
  end-page: 405
  ident: BIB19
  article-title: A new approach to convergence acceleration methods
  publication-title: Nonlinear Numerical Methods and Rational Approximation
– year: 1951
  ident: BIB42
  article-title: Numerische Behandlung von Differentialgleichungen
– volume: 9
  start-page: 1
  year: 1892
  end-page: 93
  ident: BIB99
  article-title: Sur la représentation approchée d'une fonction par des fractions rationnelles
  publication-title: Ann. Sci. Ec. Norm. Sup.
– volume: 77
  start-page: 18
  year: 1873
  end-page: 24
  ident: BIB64
  article-title: Sur la fonction exponentielle
  publication-title: C. R. Acad. Sci. Paris
– volume: 210
  start-page: 307
  year: 1910
  end-page: 357
  ident: BIB104
  article-title: The approximate arithmetical solution by finite difference of physical problems involving differential equations, with an application to the stress in a masonry dam
  publication-title: Philos. Trans. Roy. Soc. London Ser. A
– volume: 46
  start-page: 289
  year: 1926
  end-page: 305
  ident: BIB2
  article-title: On Bernoulli's numerical solution of algebraic equations
  publication-title: Proc. R. Soc. Edinb.
– reference: , to appear.
– volume: 8
  start-page: 1
  year: 1966
  end-page: 13
  ident: BIB37
  article-title: Numerical treatment of ordinary differential equations by extrapolation methods
  publication-title: Numer. Math.
– volume: 34
  start-page: 1
  year: 1955
  end-page: 42
  ident: BIB116
  article-title: Non linear transformations of divergent and slowly convergent sequences
  publication-title: J. Math. Phys.
– volume: 2
  start-page: 1
  year: 1989
  end-page: 26
  ident: BIB21
  article-title: A survey of iterative extrapolation by the
  publication-title: Det Kong. Norske Vid. Selsk. Skr.
– year: 1994
  ident: BIB41
  article-title: Histoire d'Algorithmes
– volume: 16
  start-page: 150
  year: 1976
  end-page: 161
  ident: BIB89
  article-title: Lower estimates for the error of the best uniform approximation
  publication-title: J. Approx. Theory
– volume: 37
  start-page: 197
  year: 1981
  end-page: 204
  ident: BIB45
  article-title: Automatic selection of sequence transformations
  publication-title: Math. Comp.
– year: 1994
  ident: BIB92
  article-title: Physique théorique: les approximants de Padé retrouvés
  publication-title: Approximants de Padé
– start-page: 119
  year: 1961
  end-page: 129
  ident: BIB6
  article-title: La méthode d'intégration numérique de Romberg
  publication-title: Colloque sur l'Analyse Numérique
– volume: 765
  start-page: 36
  year: 1979
  end-page: 60
  ident: BIB43
  article-title: Démonstration algébrique de l'extension de l'identité de Wynn aux tables de Padé non normales
  publication-title: Padé Approximation and its Applications
– volume: 30
  start-page: 28
  year: 1902
  end-page: 36
  ident: BIB91
  article-title: Sur les fractions continues algébriques
  publication-title: Bull. Soc. Math. France
– volume: 7
  start-page: 369
  year: 1941
  end-page: 383
  ident: BIB113
  article-title: On the numerical solution of linear simultaneous equations by an iterative method
  publication-title: Phil. Mag.
– volume: 13
  start-page: 435
  year: 1971
  end-page: 490
  ident: BIB69
  article-title: Survey of extrapolation processes in numerical analysis
  publication-title: SIAM Rev.
– year: 1987
  ident: BIB44
  article-title: Nonlinear Methods in Numerical Analysis
– year: 1992
  ident: BIB78
  article-title: Continued Fractions with Applications
– volume: 22
  start-page: 71
  year: 1988
  end-page: 88
  ident: BIB118
  article-title: Extrapolation vs. projection methods for linear systems of equations
  publication-title: J. Comput. Appl. Math.
– volume: 92
  year: 1991
  ident: BIB96
  article-title: Rational Approximations and Orthogonality
  publication-title: Trans. Math. Monographs
– volume: 7
  start-page: 225
  year: 1994
  end-page: 251
  ident: BIB112
  article-title: Non-commutative extrapolation algorithms
  publication-title: Numerical Algor.
– volume: 52
  start-page: 663
  year: 1956
  end-page: 671
  ident: BIB133
  article-title: On a procrustean technique for the numerical transformation of slowly convergent sequences and series
  publication-title: Proc. Cambridge Phil. Soc.
– volume: I
  year: 1987
  ident: BIB8
  article-title: Etude de Certaines Généralisations du
  publication-title: Thèse 3ème cycle
– volume: 8
  start-page: 11
  year: 1991
  end-page: 23
  ident: BIB28
  article-title: Construction of extrapolation processes
  publication-title: Appl. Numer. Math.
– year: 1742
  ident: BIB82
  article-title: Treatise of Fluxions
– volume: 7
  start-page: 236
  year: 1776
  end-page: 264
  ident: BIB71
  article-title: Sur l'usage des fractions continues dans le calcul intégral
  publication-title: Nouveaux Mém. Acad. Sci. Berlin
– volume: 5
  start-page: 37
  year: 1968
  end-page: 50
  ident: BIB100
  article-title: Le transformazioni razionali di una successione
  publication-title: Calcolo
– volume: 28
  start-page: 30
  year: 1955
  end-page: 36
  ident: BIB106
  article-title: Vereinfachte numerische Integration
  publication-title: Kgl. Norske Vid. Selsk. Forsk.
– volume: 34
  start-page: 361
  year: 1991
  end-page: 383
  ident: BIB36
  article-title: Sequences of transformations and triangular recursion schemes with applications in numerical analysis
  publication-title: J. Comput. Appl. Math.
– volume: 2
  start-page: 319
  year: 1994
  end-page: 341
  ident: BIB102
  article-title: Acceleration property for the
  publication-title: Adv. Comput. Math.
– volume: 12
  start-page: 317
  year: 1975
  end-page: 360
  ident: BIB14
  article-title: Généralisation de la transformation de Shanks, de la table de Padé et de l'ϵ-algorithme
  publication-title: Calcolo
– volume: 226
  start-page: 299
  year: 1927
  end-page: 349
  ident: BIB105
  article-title: The deferred approach to the limit, I: Single lattice
  publication-title: Philos. Trans. Roy. Soc. London Ser. A
– volume: 7
  start-page: 33
  year: 1994
  end-page: 73
  ident: BIB30
  article-title: Treatment of near-breakdown in the CGS algorithm
  publication-title: Numerical Algor.
– volume: 24
  start-page: 177
  year: 1975
  end-page: 184
  ident: BIB114
  article-title: Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen
  publication-title: Numer. Math.
– volume: 36
  start-page: 385
  year: 1991
  end-page: 398
  ident: BIB67
  article-title: Some results about vector extrapolation methods and related fixed-point iterations
  publication-title: J. Comput. Appl. Math.
– volume: 20
  start-page: 1099
  year: 1983
  end-page: 1105
  ident: BIB26
  article-title: Convergence acceleration by extraction of linear subsequences
  publication-title: SIAM J. Numer. Anal.
– volume: 35
  start-page: 443
  year: 1980
  end-page: 457
  ident: BIB47
  article-title: Résultats négatifs en accéleration de la convergence
  publication-title: Numer. Math.
– volume: 256
  start-page: 1435
  year: 1963
  end-page: 1437
  ident: BIB73
  article-title: Un théorème de convergence pour le procédé d'extrapolation de Richardson
  publication-title: C. R. Acad. Sci. Paris
– reference: C. Brezinski and A.C. Matos, A derivation of extrapolation algorithms based on error estimates,
– year: 1654
  ident: BIB65
  article-title: De circuli magnitudine inventa
  publication-title: Euvres
– volume: 28
  start-page: 731
  year: 1974
  end-page: 741
  ident: BIB34
  article-title: The solution of systems of equations using the vector ϵ-algorithm, and an application to boundary value problems
  publication-title: Math. Comp.
– volume: 3
  start-page: 175
  year: 1963
  end-page: 195
  ident: BIB135
  article-title: Singular rules for certain nonlinear algorithms
  publication-title: BIT
– volume: 5
  start-page: 122
  year: 1965
  end-page: 132
  ident: BIB98
  article-title: Extended Aitken acceleration
  publication-title: BIT
– year: 1936
  ident: BIB70
  article-title: Das Grenzgebiet der Elementaren und Höheren Mathematik
– start-page: 437
  year: 1989
  end-page: 441
  ident: BIB40
  article-title: On a general epsilon algorithm
  publication-title: Numerical and Applied Mathematics
– volume: 10
  start-page: 91
  year: 1956
  end-page: 96
  ident: BIB132
  article-title: On a device for computing the
  publication-title: MTAC
– volume: 1
  start-page: 531
  year: 1985
  end-page: 544
  ident: BIB9
  article-title: Sequence transformations as statistical tools
  publication-title: Appl. Numer. Math.
– volume: 11
  start-page: 3
  year: 1984
  end-page: 21
  ident: BIB50
  article-title: Richardson-extrapolation and Romberg-integration
  publication-title: Historia Math.
– year: 1991
  ident: BIB61
  article-title: Solving Ordinary Differential Equations
– reference: G. Walz,
– volume: 6
  start-page: 387
  year: 1955
  ident: 10.1016/0168-9274(95)00110-7_BIB108
  article-title: Bestimmung der Eigenwerte und Eigenvektoren einer Matrix mit Hilfe des Quotienten-Differenzen-Algorithmus
  publication-title: Z. Angew. Math. Phys.
  doi: 10.1007/BF01589764
– year: 1990
  ident: 10.1016/0168-9274(95)00110-7_BIB59
  article-title: The unsymmetric Lanczos algorithms and their relations to Padé approximation, continued fractions, and the qd algorithm
– year: 1980
  ident: 10.1016/0168-9274(95)00110-7_BIB68
– volume: 92
  year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB96
  article-title: Rational Approximations and Orthogonality
– ident: 10.1016/0168-9274(95)00110-7_BIB27
  doi: 10.1016/0377-0427(95)00157-3
– volume: 16
  start-page: 150
  year: 1976
  ident: 10.1016/0168-9274(95)00110-7_BIB89
  article-title: Lower estimates for the error of the best uniform approximation
  publication-title: J. Approx. Theory
  doi: 10.1016/0021-9045(76)90044-7
– year: 1892
  ident: 10.1016/0168-9274(95)00110-7_BIB87
– volume: 11
  start-page: 3
  year: 1984
  ident: 10.1016/0168-9274(95)00110-7_BIB50
  article-title: Richardson-extrapolation and Romberg-integration
  publication-title: Historia Math.
  doi: 10.1016/0315-0860(84)90002-8
– volume: 77
  start-page: 18
  year: 1873
  ident: 10.1016/0168-9274(95)00110-7_BIB64_1
  article-title: Sur la fonction exponentielle
  publication-title: C. R. Acad. Sci. Paris
– volume: 77
  start-page: 226
  year: 1873
  ident: 10.1016/0168-9274(95)00110-7_BIB64_3
  article-title: Sur la fonction exponentielle
  publication-title: C. R. Acad. Sci. Paris
– start-page: 73
  year: 1985
  ident: 10.1016/0168-9274(95)00110-7_BIB125
  article-title: Vector Padé approximants
– volume: 24
  start-page: 1212
  year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB52
  article-title: An algorithm for a generalization of the Richardson extrapolation process
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0724080
– volume: 2
  start-page: 309
  year: 1903
  ident: 10.1016/0168-9274(95)00110-7_BIB90
  article-title: Extension of Huygen's approximation to a circular arc
  publication-title: Math. Gaz.
  doi: 10.2307/3605128
– volume: 2 vols
  year: 1981
  ident: 10.1016/0168-9274(95)00110-7_BIB5_1
– year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB41
– volume: 19
  start-page: 204
  year: 1979
  ident: 10.1016/0168-9274(95)00110-7_BIB60
  article-title: Generalized Neville type extrapolation schemes
  publication-title: BIT
  doi: 10.1007/BF01930850
– volume: 50
  year: 1980
  ident: 10.1016/0168-9274(95)00110-7_BIB16
  article-title: Padé-Type Approximation and General Orthogonal Polynomials
– volume: R1
  start-page: 84
  year: 1973
  ident: 10.1016/0168-9274(95)00110-7_BIB54
  article-title: Transformations de suites
  publication-title: RAIRO
  doi: 10.1051/m2an/197307R100841
– ident: 10.1016/0168-9274(95)00110-7_BIB85
– year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB38
– year: 1981
  ident: 10.1016/0168-9274(95)00110-7_BIB131
– year: 1951
  ident: 10.1016/0168-9274(95)00110-7_BIB42
– volume: 59
  start-page: 147
  year: 1876
  ident: 10.1016/0168-9274(95)00110-7_BIB94_1
  article-title: Studien zu Fürstenau's neuer Methode der Darstellung und Berechnung der Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten
  publication-title: Arch. Math. Phys.
– volume: 52
  start-page: 663
  year: 1956
  ident: 10.1016/0168-9274(95)00110-7_BIB133
  article-title: On a procrustean technique for the numerical transformation of slowly convergent sequences and series
– year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB61
– volume: I
  year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB8
  article-title: Etude de Certaines Généralisations du Δ2 d'Aitken et Comparaison de Procédés d'Accélération de la Convergence
– volume: 2
  start-page: 1
  year: 1989
  ident: 10.1016/0168-9274(95)00110-7_BIB21
  article-title: A survey of iterative extrapolation by the E-algorithm
  publication-title: Det Kong. Norske Vid. Selsk. Skr.
– volume: 7
  start-page: 236
  year: 1776
  ident: 10.1016/0168-9274(95)00110-7_BIB71_1
  article-title: Sur l'usage des fractions continues dans le calcul intégral
  publication-title: Nouveaux Mém. Acad. Sci. Berlin
– volume: 5
  start-page: 122
  year: 1965
  ident: 10.1016/0168-9274(95)00110-7_BIB98
  article-title: Extended Aitken acceleration
  publication-title: BIT
  doi: 10.1007/BF01939615
– volume: 7
  start-page: 33
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB30
  article-title: Treatment of near-breakdown in the CGS algorithm
  publication-title: Numerical Algor.
  doi: 10.1007/BF02141260
– volume: 190
  start-page: 71
  year: 1993
  ident: 10.1016/0168-9274(95)00110-7_BIB110
  article-title: Quasilinear vector extrapolation methods
  publication-title: Linear Alg. Appl.
  doi: 10.1016/0024-3795(93)90220-I
– volume: 28
  start-page: 30
  year: 1955
  ident: 10.1016/0168-9274(95)00110-7_BIB106
  article-title: Vereinfachte numerische Integration
  publication-title: Kgl. Norske Vid. Selsk. Forsk.
– volume: 210
  start-page: 307
  year: 1910
  ident: 10.1016/0168-9274(95)00110-7_BIB104
  article-title: The approximate arithmetical solution by finite difference of physical problems involving differential equations, with an application to the stress in a masonry dam
  publication-title: Philos. Trans. Roy. Soc. London Ser. A
  doi: 10.1098/rsta.1911.0009
– volume: 19
  start-page: 141
  year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB126
  article-title: Vector orthogonal relations. Vector QD algorithm
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/0377-0427(87)90182-8
– volume: 68
  start-page: 549
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB127
  article-title: Convergence of vectorial sequences. Applications
  publication-title: Numer. Math.
  doi: 10.1007/s002110050075
– start-page: 373
  year: 1988
  ident: 10.1016/0168-9274(95)00110-7_BIB19
  article-title: A new approach to convergence acceleration methods
– volume: 8
  start-page: 1
  year: 1966
  ident: 10.1016/0168-9274(95)00110-7_BIB37
  article-title: Numerical treatment of ordinary differential equations by extrapolation methods
  publication-title: Numer. Math.
  doi: 10.1007/BF02165234
– volume: 202
  year: 1988
  ident: 10.1016/0168-9274(95)00110-7_BIB79
  article-title: Strong Asymptotics for Extremal Errors and Polynomials Associated with Erdõs-type Weights
– volume: 22
  start-page: 71
  year: 1988
  ident: 10.1016/0168-9274(95)00110-7_BIB118
  article-title: Extrapolation vs. projection methods for linear systems of equations
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/0377-0427(88)90289-0
– volume: 1265
  year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB124
  article-title: Asymptotics for Orthogonal Polynomials
– volume: 2
  start-page: 461
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB31
  article-title: A general extrapolation procedure revisited
  publication-title: Adv. Comput. Math.
  doi: 10.1007/BF02521609
– year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB44
– volume: 37
  start-page: 197
  year: 1981
  ident: 10.1016/0168-9274(95)00110-7_BIB45
  article-title: Automatic selection of sequence transformations
  publication-title: Math. Comp.
  doi: 10.1090/S0025-5718-1981-0616372-5
– volume: 271 A
  start-page: 1174
  year: 1970
  ident: 10.1016/0168-9274(95)00110-7_BIB12
  article-title: Application de l'ϵ-algorithme à la résoltion des systèmes non linéaires
  publication-title: C. R. Acad. Sci. Paris
– year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB128
  article-title: The history of extrapolation methods in numerical analysis
– volume: 34
  start-page: 361
  year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB36
  article-title: Sequences of transformations and triangular recursion schemes with applications in numerical analysis
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/0377-0427(91)90095-2
– volume: 16
  start-page: 301
  year: 1962
  ident: 10.1016/0168-9274(95)00110-7_BIB134
  article-title: Acceleration techniques for iterated vector and matrix problems
  publication-title: Math. Comp.
  doi: 10.1090/S0025-5718-1962-0145647-X
– volume: 3
  start-page: 3
  year: 1926
  ident: 10.1016/0168-9274(95)00110-7_BIB10
  article-title: On Rayleigh's principle in the theory of differential equations of mathematical physics and upon Euler's method in the calculus of variation
  publication-title: Acad. Sci. Ukraine (Phys. Math.)
– volume: vol. 4
  start-page: 127
  year: 1904
  ident: 10.1016/0168-9274(95)00110-7_BIB3_1
  article-title: Interpolation
– volume: 35
  start-page: 443
  year: 1980
  ident: 10.1016/0168-9274(95)00110-7_BIB47
  article-title: Résultats négatifs en accéleration de la convergence
  publication-title: Numer. Math.
  doi: 10.1007/BF01399010
– volume: 86
  start-page: 61
  year: 1988
  ident: 10.1016/0168-9274(95)00110-7_BIB20
  article-title: Quasi-linear extrapolation processes
– year: 1654
  ident: 10.1016/0168-9274(95)00110-7_BIB65
  article-title: De circuli magnitudine inventa
  publication-title: Euvres
– volume: vol. 4
  year: 1993
  ident: 10.1016/0168-9274(95)00110-7_BIB3_2
  article-title: Interpolation
– year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB92
  article-title: Physique théorique: les approximants de Padé retrouvés
– volume: 36
  start-page: 385
  year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB67
  article-title: Some results about vector extrapolation methods and related fixed-point iterations
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/0377-0427(91)90018-F
– volume: 124
  start-page: 768
  year: 1961
  ident: 10.1016/0168-9274(95)00110-7_BIB4
  article-title: Application of the Padé method to the investigation of some magnetic properties of the Ising model
  publication-title: Phys. Rev.
  doi: 10.1103/PhysRev.124.768
– volume: 1305
  year: 1988
  ident: 10.1016/0168-9274(95)00110-7_BIB80
  article-title: Strong Asymptotics for Extremal Polynomials Associated with Weights on R
– year: 1742
  ident: 10.1016/0168-9274(95)00110-7_BIB82
– volume: 5
  start-page: 48
  year: 1963
  ident: 10.1016/0168-9274(95)00110-7_BIB109
  article-title: Ausdehnung des Rombergschen Prinzips
  publication-title: Numer. Math.
  doi: 10.1007/BF01385877
– volume: 5
  start-page: 37
  year: 1968
  ident: 10.1016/0168-9274(95)00110-7_BIB100
  article-title: Le transformazioni razionali di una successione
  publication-title: Calcolo
  doi: 10.1007/BF02575564
– volume: 42
  start-page: 331
  year: 1983
  ident: 10.1016/0168-9274(95)00110-7_BIB57
  article-title: Vector valued rational interpolants I
  publication-title: Numer. Math.
  doi: 10.1007/BF01389578
– volume: 8
  start-page: 11
  year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB28
  article-title: Construction of extrapolation processes
  publication-title: Appl. Numer. Math.
  doi: 10.1016/0168-9274(91)90095-H
– volume: 2
  start-page: 130
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB25
  article-title: The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer
  publication-title: Elect. Trans. Numer. Anal.
– volume: 28
  start-page: 731
  year: 1974
  ident: 10.1016/0168-9274(95)00110-7_BIB34
  article-title: The solution of systems of equations using the vector ϵ-algorithm, and an application to boundary value problems
  publication-title: Math. Comp.
– volume: 77
  start-page: 285
  year: 1873
  ident: 10.1016/0168-9274(95)00110-7_BIB64_4
  article-title: Sur la fonction exponentielle
  publication-title: C. R. Acad. Sci. Paris
– volume: 1002
  year: 1983
  ident: 10.1016/0168-9274(95)00110-7_BIB51
  article-title: Zeros of Sections of Power Series
– ident: 10.1016/0168-9274(95)00110-7_BIB129
– volume: 49
  start-page: 23
  year: 1958
  ident: 10.1016/0168-9274(95)00110-7_BIB63
  article-title: The quotient-difference algorithm
  publication-title: Nat. Bur. Stand. Appl. Math. Ser.
– volume: 7
  start-page: 225
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB112
  article-title: Non-commutative extrapolation algorithms
  publication-title: Numerical Algor.
  doi: 10.1007/BF02140685
– year: 1987
  ident: 10.1016/0168-9274(95)00110-7_BIB49
– volume: B3
  start-page: 371
  year: 1973
  ident: 10.1016/0168-9274(95)00110-7_BIB76
  article-title: Development of nonlinear transformations for improving convergence of sequences
  publication-title: Int. J. Comput. Math.
– volume: 2
  start-page: 393
  year: 1992
  ident: 10.1016/0168-9274(95)00110-7_BIB86
  article-title: Acceleration property for the columns of the E-algorithm
  publication-title: Numerical Algor.
  doi: 10.1007/BF02139476
– volume: 3
  start-page: 175
  year: 1963
  ident: 10.1016/0168-9274(95)00110-7_BIB135
  article-title: Singular rules for certain nonlinear algorithms
  publication-title: BIT
  doi: 10.1007/BF01939985
– year: 1949
  ident: 10.1016/0168-9274(95)00110-7_BIB115
– volume: 3
  start-page: 65
  year: 1983
  ident: 10.1016/0168-9274(95)00110-7_BIB17
  article-title: Error control in convergence acceleration processes
  publication-title: IMA J. Numer. Anal.
  doi: 10.1093/imanum/3.1.65
– volume: 15
  start-page: 77
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB74
  article-title: On the stochastic acceleration of sequences of random variables
  publication-title: Appl. Numer. Math.
  doi: 10.1016/0168-9274(94)00026-3
– volume: 32
  start-page: 258
  year: 1900
  ident: 10.1016/0168-9274(95)00110-7_BIB117
  article-title: Some quadrature formulas
– year: 1859
  ident: 10.1016/0168-9274(95)00110-7_BIB111
– volume: 273 A
  start-page: 727
  year: 1971
  ident: 10.1016/0168-9274(95)00110-7_BIB13
  article-title: Accélération de suites à convergence logarithmique
  publication-title: C. R. Acad. Sci. Paris
– year: 1947
  ident: 10.1016/0168-9274(95)00110-7_BIB97
– year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB24
– volume: 20
  start-page: 1099
  year: 1983
  ident: 10.1016/0168-9274(95)00110-7_BIB26
  article-title: Convergence acceleration by extraction of linear subsequences
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0720079
– volume: 30
  start-page: 127
  year: 1845
  ident: 10.1016/0168-9274(95)00110-7_BIB66
  article-title: Über die Darstellung einer Reihe gegebener Werthe durch eine gebrochen rationale Funktion
  publication-title: J. Reine Angew. Math.
– volume: 226
  start-page: 299
  year: 1927
  ident: 10.1016/0168-9274(95)00110-7_BIB105
  article-title: The deferred approach to the limit, I: Single lattice
  publication-title: Philos. Trans. Roy. Soc. London Ser. A
  doi: 10.1098/rsta.1927.0008
– start-page: 200
  year: 1976
  ident: 10.1016/0168-9274(95)00110-7_BIB93
  article-title: Neville-Aitken algorithms for interpolating by functions of Čebyšev-systems in the sense of Newton and in a generalized sense of Hermite
– year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB23
– year: 1936
  ident: 10.1016/0168-9274(95)00110-7_BIB70
– year: 1861
  ident: 10.1016/0168-9274(95)00110-7_BIB62
  article-title: Ueber eine besondere Classe der symmetrischen Determinanten
– volume: 57
  start-page: 365
  year: 1990
  ident: 10.1016/0168-9274(95)00110-7_BIB119
  article-title: On a generalization of the Richardson extrapolation process
  publication-title: Numer. Math.
  doi: 10.1007/BF01386416
– volume: 765
  start-page: 36
  year: 1979
  ident: 10.1016/0168-9274(95)00110-7_BIB43
  article-title: Démonstration algébrique de l'extension de l'identité de Wynn aux tables de Padé non normales
– volume: 26
  start-page: 427
  year: 1972
  ident: 10.1016/0168-9274(95)00110-7_BIB53
  article-title: On the solution of systems of equations by the epsilon algorithm of Wynn
  publication-title: Math. Comp.
  doi: 10.1090/S0025-5718-1972-0314226-X
– year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB29
– year: 1988
  ident: 10.1016/0168-9274(95)00110-7_BIB46
– volume: 24
  start-page: 177
  year: 1975
  ident: 10.1016/0168-9274(95)00110-7_BIB114
  article-title: Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen
  publication-title: Numer. Math.
  doi: 10.1007/BF01400966
– volume: 46
  start-page: 289
  year: 1926
  ident: 10.1016/0168-9274(95)00110-7_BIB2
  article-title: On Bernoulli's numerical solution of algebraic equations
– volume: 974
  year: 1983
  ident: 10.1016/0168-9274(95)00110-7_BIB48
  article-title: Polynômes Orthogonaux Formels. Applications
– volume: 1
  start-page: 531
  year: 1985
  ident: 10.1016/0168-9274(95)00110-7_BIB9
  article-title: Sequence transformations as statistical tools
  publication-title: Appl. Numer. Math.
  doi: 10.1016/0168-9274(85)90036-4
– volume: 256
  start-page: 1435
  year: 1963
  ident: 10.1016/0168-9274(95)00110-7_BIB73
  article-title: Un théorème de convergence pour le procédé d'extrapolation de Richardson
  publication-title: C. R. Acad. Sci. Paris
– year: 1990
  ident: 10.1016/0168-9274(95)00110-7_BIB22
– volume: 3
  start-page: 128
  year: 1758
  ident: 10.1016/0168-9274(95)00110-7_BIB72
  article-title: Observationes variae in mathesin puram
  publication-title: Acta Helvetica
– volume: 12
  start-page: 317
  year: 1975
  ident: 10.1016/0168-9274(95)00110-7_BIB14
  article-title: Généralisation de la transformation de Shanks, de la table de Padé et de l'ϵ-algorithme
  publication-title: Calcolo
  doi: 10.1007/BF02575753
– volume: 7
  start-page: 369
  year: 1941
  ident: 10.1016/0168-9274(95)00110-7_BIB113
  article-title: On the numerical solution of linear simultaneous equations by an iterative method
  publication-title: Phil. Mag.
  doi: 10.1080/14786444108520797
– year: 1992
  ident: 10.1016/0168-9274(95)00110-7_BIB78
– start-page: 119
  year: 1961
  ident: 10.1016/0168-9274(95)00110-7_BIB6
  article-title: La méthode d'intégration numérique de Romberg
– volume: 48
  start-page: 228
  year: 1952
  ident: 10.1016/0168-9274(95)00110-7_BIB81
  article-title: A method of summing infinite series
  publication-title: J. Res. Nat. Bur. Stand.
  doi: 10.6028/jres.048.032
– volume: 2 vols.
  year: 1996
  ident: 10.1016/0168-9274(95)00110-7_BIB5_2
– volume: 46
  start-page: 311
  year: 1985
  ident: 10.1016/0168-9274(95)00110-7_BIB18
  article-title: Composite sequence transformations
  publication-title: Numer. Math.
  doi: 10.1007/BF01389488
– volume: 13
  start-page: 435
  year: 1971
  ident: 10.1016/0168-9274(95)00110-7_BIB69
  article-title: Survey of extrapolation processes in numerical analysis
  publication-title: SIAM Rev.
  doi: 10.1137/1013092
– volume: 2
  start-page: 319
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB102
  article-title: Acceleration property for the E-algorithm and an application to the summation of series
  publication-title: Adv. Comput. Math.
  doi: 10.1007/BF02521114
– volume: 8
  start-page: 1
  year: 1894
  ident: 10.1016/0168-9274(95)00110-7_BIB123
  article-title: Recherches sur les fractions continues
  publication-title: Ann. Fac. Sci. Toulouse
  doi: 10.5802/afst.108
– volume: 41
  start-page: 408
  year: 1961
  ident: 10.1016/0168-9274(95)00110-7_BIB121
  article-title: Altes und neues über numerische Quadratur
  publication-title: Z. Angew. Math. Mech.
  doi: 10.1002/zamm.19610411003
– start-page: 443
  year: 1989
  ident: 10.1016/0168-9274(95)00110-7_BIB7
  article-title: A connection between the E-algorithm and the epsilon-algorithm
– year: 1993
  ident: 10.1016/0168-9274(95)00110-7_BIB103
– volume: 61
  start-page: 19
  year: 1877
  ident: 10.1016/0168-9274(95)00110-7_BIB94_2
  article-title: Studien zu Fürstenau's neuer Methode der Darstellung und Berechnung der Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten
  publication-title: Arch. Math. Phys.
– volume: 77
  start-page: 74
  year: 1873
  ident: 10.1016/0168-9274(95)00110-7_BIB64_2
  article-title: Sur la fonction exponentielle
  publication-title: C. R. Acad. Sci. Paris
– volume: Vol. III
  start-page: 47
  year: 1994
  ident: 10.1016/0168-9274(95)00110-7_BIB35
  article-title: Padé approximations
– year: 1965
  ident: 10.1016/0168-9274(95)00110-7_BIB1
– volume: I
  year: 1978
  ident: 10.1016/0168-9274(95)00110-7_BIB55
  article-title: Estimation de la Limite de Suites et Formalisation de Procédés d'Accélération de la Convergence
– start-page: 437
  year: 1989
  ident: 10.1016/0168-9274(95)00110-7_BIB40
  article-title: On a general epsilon algorithm
– volume: 10
  start-page: 189
  year: 1989
  ident: 10.1016/0168-9274(95)00110-7_BIB130
  article-title: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
  publication-title: Comput. Physics Reports
  doi: 10.1016/0167-7977(89)90011-7
– year: 1983
  ident: 10.1016/0168-9274(95)00110-7_BIB83
– volume: 35
  start-page: 175
  year: 1980
  ident: 10.1016/0168-9274(95)00110-7_BIB15
  article-title: A general extrapolation algorithm
  publication-title: Numer. Math.
  doi: 10.1007/BF01396314
– volume: 5
  start-page: 233
  year: 1954
  ident: 10.1016/0168-9274(95)00110-7_BIB107
  article-title: Der Quotienten-Differenzen-Algorithmus
  publication-title: Z. Angew. Math. Phys.
  doi: 10.1007/BF01600331
– volume: 20
  start-page: 213
  year: 1882
  ident: 10.1016/0168-9274(95)00110-7_BIB77
  article-title: Ueber die Zahl π
  publication-title: Math. Ann.
  doi: 10.1007/BF01446522
– volume: 1
  start-page: 261
  year: 1991
  ident: 10.1016/0168-9274(95)00110-7_BIB32
  article-title: Avoiding breakdown and near-breakdown in Lanczos type algorithms
  publication-title: Numerical Algor.
  doi: 10.1007/BF02142326
– year: 1990
  ident: 10.1016/0168-9274(95)00110-7_BIB95
– year: 1972
  ident: 10.1016/0168-9274(95)00110-7_BIB101
– volume: 34
  start-page: 1
  year: 1955
  ident: 10.1016/0168-9274(95)00110-7_BIB116
  article-title: Non linear transformations of divergent and slowly convergent sequences
  publication-title: J. Math. Phys.
  doi: 10.1002/sapm19553411
– volume: 58
  start-page: 329
  year: 1990
  ident: 10.1016/0168-9274(95)00110-7_BIB84
  article-title: Acceleration methods based on convergence tests
  publication-title: Numer. Math.
  doi: 10.1007/BF01385628
– volume: 4
  start-page: 301
  year: 1869
  ident: 10.1016/0168-9274(95)00110-7_BIB71_2
  article-title: Sur l'usage des fractions continues dans le calcul intégral
  publication-title: Oeuvres
– volume: 30
  start-page: 28
  year: 1902
  ident: 10.1016/0168-9274(95)00110-7_BIB91
  article-title: Sur les fractions continues algébriques
  publication-title: Bull. Soc. Math. France
  doi: 10.24033/bsmf.653
– volume: 8
  start-page: 365
  year: 1971
  ident: 10.1016/0168-9274(95)00110-7_BIB58
  article-title: Higher order G-transformations
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0708037
– volume: 3
  start-page: 273
  year: 1992
  ident: 10.1016/0168-9274(95)00110-7_BIB75
  article-title: Convergence of the topological ϵ-algorithm for solving systems of nonlinear equations
  publication-title: Numerical Algor.
  doi: 10.1007/BF02141936
– volume: 52
  start-page: 215
  year: 1956
  ident: 10.1016/0168-9274(95)00110-7_BIB11
  article-title: Eigenvalues of differential equations by finite-difference methods
– volume: 7
  start-page: 17
  year: 1971
  ident: 10.1016/0168-9274(95)00110-7_BIB88
  article-title: A note on the ϵ-algorithm
  publication-title: Computing
  doi: 10.1007/BF02279938
– volume: 10
  start-page: 91
  year: 1956
  ident: 10.1016/0168-9274(95)00110-7_BIB132
  article-title: On a device for computing the em(Sn) transformation
  publication-title: MTAC
– year: 1992
  ident: 10.1016/0168-9274(95)00110-7_BIB120
– volume: 63
  start-page: 29
  year: 1992
  ident: 10.1016/0168-9274(95)00110-7_BIB33
  article-title: A breakdown-free Lanczos type algorithm for solving linear systems
  publication-title: Numer. Math.
  doi: 10.1007/BF01385846
– volume: 84
  start-page: 242
  year: 1878
  ident: 10.1016/0168-9274(95)00110-7_BIB39
  article-title: Ein Beitrag zur Mannigfaltigkeitslehre
  publication-title: J. Reine Angew. Math.
  doi: 10.1515/crll.1878.84.242
– volume: 9
  start-page: 1
  year: 1892
  ident: 10.1016/0168-9274(95)00110-7_BIB99_1
  article-title: Sur la représentation approchée d'une fonction par des fractions rationnelles
  publication-title: Ann. Sci. Ec. Norm. Sup.
– start-page: 72
  year: 1984
  ident: 10.1016/0168-9274(95)00110-7_BIB99_2
– volume: 2
  start-page: 384
  year: 1965
  ident: 10.1016/0168-9274(95)00110-7_BIB56
  article-title: On extrapolation algorithms for initial-value problems
  publication-title: SIAM J. Numer. Anal.
– volume: 3
  start-page: H.1
  year: 1889
  ident: 10.1016/0168-9274(95)00110-7_BIB122
  article-title: Sur la réduction en fraction continue d'une série procédant suivant les puissances descendantes d'une variable
  publication-title: Ann. Fac. Sci. Toulouse
  doi: 10.5802/afst.34
SSID ssj0005540
Score 1.7123808
Snippet In numerical analysis there are many methods producing sequences. Such is the case of iterative methods, of methods involving series expansions, of...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 299
Title Extrapolation algorithms and Padé approximations: a historical survey
URI https://dx.doi.org/10.1016/0168-9274(95)00110-7
Volume 20
WOSCitedRecordID wos0168927495001107&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1873-5460
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0005540
  issn: 0168-9274
  databaseCode: AIEXJ
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1NT9swGLYG7MBlg21obAP5wKRNyCN24rjmhlAR44A4MKm3yHUcQCpplbSo2j_a79gf2-vYTtqB2DhwiSLLH5Ef5_Vrvx8PQns55SLRQhMQfIYkQx2TYZoXpEg1Z1JRWkSqIZsQ5-e9wUBeeP7OuqETEGXZm8_l5FmhhjIA24bOPgHutlMogHcAHZ4AOzz_C_j-fFqpydj5uO2r0dUYzv_Xty4X8wUg2pjGXTLx-Y2LXKxdzPN1lzOknlV3yybfoK-WM2fkGe3ftilfu7v2yvxsubCPv3V3Cs4NOThVhWvGFMQgc_w5QU6yaGE9xItCz1Ec-f0zdvL0nmh2twRtz6A_S_6ZySZpHRHddhRM8H_tUq3vYHBLsz1ltqdM8sYzL8rEClpjgkuQbmtH3_uDs87Zhzehse3oIYiSpgdt2RfJv_qveVhJWVA8LjfQK39iwEcO6U30wpRv0GuPBvayuX6LTpaAxx3wGIDHAPzvX3gZ9EOscAc5dpC_Qz9O-pfHp8SzZBAdi2hKaFwURjEF53qlqElyqiJh_0yTKGvTtSpgzI2h-RCOtkkKtaWOcmGJ3AXTPN5Cq-W4NO8RTjRlohfJSMgh6ClaFTZ1EWOWRDU3ebKN4jAtmfYp5C2TySh7DJRtRNpWE5dC5R_1RZjxzKuBTr3LYCk92vLDE0f6iNa71f8JrU6rmdlBL_Xd9Kaudv0a-gMUK3dg
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Extrapolation+algorithms+and+Pad%C3%A9+approximations%3A+a+historical+survey&rft.jtitle=Applied+numerical+mathematics&rft.au=Brezinski%2C+C.&rft.date=1996-03-01&rft.issn=0168-9274&rft.volume=20&rft.issue=3&rft.spage=299&rft.epage=318&rft_id=info:doi/10.1016%2F0168-9274%2895%2900110-7&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_0168_9274_95_00110_7
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-9274&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-9274&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-9274&client=summon