The epsilon algorithm and related topics
The epsilon algorithm is recommended as the best all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain its connections with Padé approximation and continued fractions which underpin its th...
Gespeichert in:
| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 122; H. 1; S. 51 - 80 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
01.10.2000
|
| Schlagworte: | |
| ISSN: | 0377-0427, 1879-1778 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The epsilon algorithm is recommended as the best
all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain its connections with Padé approximation and continued fractions which underpin its theoretical base. Then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector-valued sequences, and some related topics. In this paper, we consider the class of methods based on using generalised inverses of vectors, and the formulation specifically includes the complex case wherever possible. |
|---|---|
| AbstractList | The epsilon algorithm is recommended as the best
all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain its connections with Padé approximation and continued fractions which underpin its theoretical base. Then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector-valued sequences, and some related topics. In this paper, we consider the class of methods based on using generalised inverses of vectors, and the formulation specifically includes the complex case wherever possible. |
| Author | Salam, A. Graves-Morris, P.R. Roberts, D.E. |
| Author_xml | – sequence: 1 givenname: P.R. surname: Graves-Morris fullname: Graves-Morris, P.R. email: p.r.graves-morris@bradford.ac.uk organization: School of Computing and Mathematics, University of Bradford, Bradford, West Yorkshire BD7 1DP, UK – sequence: 2 givenname: D.E. surname: Roberts fullname: Roberts, D.E. organization: Department of Mathematics, Napier University, Colinton Road, Edinburgh, EH14 1DJ Scotland, UK – sequence: 3 givenname: A. surname: Salam fullname: Salam, A. organization: Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, BP 699, 62228 Calais, France |
| BookMark | eNqFz01LAzEQxvEgFWyrH0HYYz2szuxukl08iJT6AgUP9h6yyayNbDclCYLf3r6IBy89zWX-D_wmbDT4gRi7RrhFQHH3DqWUOVSFnAHcAJSc53jGxljLJkcp6xEb_71csEmMnwAgGqzGbLZaU0bb6Ho_ZLr_8MGl9SbTg80C9TqRzZLfOhMv2Xmn-0hXv3fKVk-L1fwlX749v84fl7kpQaacsCoMNq3gtjYdF4RFR7xtTNlY4kVtsa3AGs6p7ch2QBIaqoSQWmhTtuWU8eOsCT7GQJ3aBrfR4VshqL1WHbRqT1EA6qBVuOvu_3XGJZ2cH1LQrj9ZPxxr2sm-HAUVjaPBkHWBTFLWuxMLP6FacII |
| CitedBy_id | crossref_primary_10_1007_s11075_018_0567_2 crossref_primary_10_1002_nme_1612 crossref_primary_10_1016_S0898_1221_03_80014_7 crossref_primary_10_1007_JHEP12_2023_056 crossref_primary_10_1088_0031_8949_81_02_025006 crossref_primary_10_1016_j_ijepes_2017_08_018 crossref_primary_10_1016_j_compstruc_2008_07_004 crossref_primary_10_1088_1751_8113_41_42_425207 crossref_primary_10_1016_j_ifacol_2022_11_053 crossref_primary_10_1016_S0377_0427_00_00360_5 crossref_primary_10_1088_1361_6455_ab46f1 crossref_primary_10_1088_1464_4258_4_4_310 crossref_primary_10_3390_a17050180 crossref_primary_10_1002_cnm_705 crossref_primary_10_1016_j_anucene_2015_01_019 crossref_primary_10_1007_s11075_019_00862_z crossref_primary_10_1016_j_jcp_2011_04_007 crossref_primary_10_1016_j_apnum_2015_03_007 crossref_primary_10_1016_j_istruc_2025_109073 crossref_primary_10_1007_s11075_019_00695_w crossref_primary_10_1007_s00466_008_0303_1 crossref_primary_10_1002_zamm_202100006 crossref_primary_10_1239_jap_1091543429 crossref_primary_10_1023_A_1014880510928 crossref_primary_10_1134_S1995423924600093 crossref_primary_10_1007_s00214_018_2238_8 crossref_primary_10_1016_j_compstruc_2009_02_009 crossref_primary_10_1017_S0021900200020581 crossref_primary_10_1007_s10409_009_0255_5 crossref_primary_10_1016_j_optcom_2010_06_030 crossref_primary_10_1002_qua_21966 crossref_primary_10_1016_j_anucene_2025_111672 crossref_primary_10_1007_s11075_016_0238_0 crossref_primary_10_1016_j_engstruct_2023_116094 |
| Cites_doi | 10.1016/S0010-4655(98)00111-8 10.1090/S0025-5718-1961-0158513-X 10.1023/A:1018952415379 10.1007/BF01451604 10.1016/S0377-0427(00)00357-5 10.1063/1.523760 10.1002/sapm19553411 10.1016/0167-7977(89)90011-7 10.1007/978-3-642-75771-6_19 10.2307/2002183 10.1137/0909056 10.1006/aphy.1996.0023 10.1016/S0024-3795(97)10091-X 10.1090/S0025-5718-1962-0145647-X 10.1016/0377-0427(88)90331-7 10.1016/S0377-0427(96)00127-6 10.1016/0377-0427(91)90092-X 10.1023/A:1018951020406 10.1098/rspa.1990.0131 10.1006/jsvi.1995.0110 10.1016/S0377-0427(00)00359-9 10.1016/S0377-0427(99)00034-5 10.1007/BF00281229 10.1023/A:1011633327892 10.1007/BF01389578 10.1007/BF01893432 10.1016/0377-0427(92)00008-W 10.1017/S0962492900002737 10.1007/BFb0085574 10.1016/0377-0427(95)00133-6 10.1006/jath.1996.3077 10.1016/S0377-0427(00)00363-0 10.1137/0703007 10.1023/A:1018944213562 10.1007/BF02142505 10.1137/0719059 10.1006/jath.1997.3263 10.1007/BF02575753 10.1007/BF01390336 10.1007/BF01406003 10.1137/0723013 10.1007/BF02279938 |
| ContentType | Journal Article |
| Copyright | 2000 Elsevier Science B.V. |
| Copyright_xml | – notice: 2000 Elsevier Science B.V. |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/S0377-0427(00)00355-1 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-1778 |
| EndPage | 80 |
| ExternalDocumentID | 10_1016_S0377_0427_00_00355_1 S0377042700003551 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAFWJ AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 D-I DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ NHB O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 UPT WUQ XPP YQT ZMT ZY4 ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c307t-e142c19b65d8cf56e12fe5b9c39de528d1b40dc55ebfedf0e709e4667a6ac3b3 |
| ISICitedReferencesCount | 45 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000089756400005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-0427 |
| IngestDate | Sat Nov 29 06:06:49 EST 2025 Tue Nov 18 22:10:15 EST 2025 Fri Feb 23 02:33:25 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Star identity Padé Designant Epsilon algorithm Cross rule Wynn qd algorithm Compass identity Vector-valued approximant |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c307t-e142c19b65d8cf56e12fe5b9c39de528d1b40dc55ebfedf0e709e4667a6ac3b3 |
| OpenAccessLink | https://dx.doi.org/10.1016/S0377-0427(00)00355-1 |
| PageCount | 30 |
| ParticipantIDs | crossref_primary_10_1016_S0377_0427_00_00355_1 crossref_citationtrail_10_1016_S0377_0427_00_00355_1 elsevier_sciencedirect_doi_10_1016_S0377_0427_00_00355_1 |
| PublicationCentury | 2000 |
| PublicationDate | 2000-10-01 |
| PublicationDateYYYYMMDD | 2000-10-01 |
| PublicationDate_xml | – month: 10 year: 2000 text: 2000-10-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2000 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Colton, Kress (BIB12) 1983 Roberts (BIB42) 1999; 105 Brezinski (BIB4) 1971; 17 Delahaye (BIB19) 1988 Roberts (BIB40) 1998; 8 Brezinski (BIB6) 1977 Baker (BIB1) 1975 K. Jbilou, H. Sadok, Vector extrapolation methods, Applications and numerical comparison, this volume, J. Comput. Appl. Math. 122 (2000) 149–165. McLeod (BIB37) 1972; 7 Wynn (BIB57) 1962; 16 Roberts (BIB38) 1990; 431 Baker, Graves-Morris (BIB2) 1996 Chandler-Wilde, Rahman, Ross (BIB11) 1998 W. Gander, E.H. Golub, D. Gruntz, Solving linear systems by extrapolation in Supercomputing, Trondheim, Computer Systems Science, Vol. 62, Springer, Berlin, 1989, pp. 279–293. H.H.H. Homeier, Scalar Levin-type sequence transformations, this volume, J. Comput. Appl. Math. 122 (2000) 81–147. Graves-Morris, Saff (BIB29) 1991; 34 Graves-Morris, Beckermann (BIB23) 1997; 7 Jones, Thron (BIB36) 1980 Gutknecht (BIB31) 1997; 6 F. Cordellier, Thesis, University of Lille, 1989. Tan (BIB49) 1988; 9 Wynn (BIB55) 1961; 15 E.J. Weniger, Prediction properties of Aitken's iterated Cuyt, Wuytack (BIB17) 1987 Brezinski (BIB8) 1980 Brezinski, Redivo-Zaglia (BIB9) 1991 Weniger (BIB50) 1989; 10 F. Cordellier, Démonstration algébrique de l'extension de l'identité de Wynn aux tables de Padé non-normales, in: L. Wuytack (Ed.), Padé Approximation and its Applications, Springer, Berlin, Lecture Notes in Mathematics, Vol. 765, 1979, pp. 36–60. Salam (BIB45) 1998; 278 F. Cordellier, L Graves-Morris, Roberts (BIB26) 1994; 51 Sidi, Ford, Smith (BIB48) 1986; 23 Salam (BIB46) 1999; 97 process, of Wynn's epsilon algorithm and of Brezinski's iterated theta algorithm, this volume, J. Comp. Appl. Math. 122 (2000) 329–356. Wimp (BIB53) 1981 algorithme vectoriel, interprétation géometrique et règles singulières, Exposé au Colloque d'Analyse Numérique de Gourette, 1974. Graves-Morris, Saff (BIB28) 1988; 23 Wynn (BIB56) 1961; 20 Chandler-Wilde, Hothersall (BIB10) 1995; 180 Roberts (BIB39) 1996; 70 Graffi, Grecchi (BIB21) 1978; 19 Berlekamp (BIB3) 1968 Weniger (BIB51) 1996; 246 Graves-Morris, Roberts (BIB27) 1997; 77 Wynn (BIB59) 1966; 3 Roberts (BIB41) 1998; 17 Wynn (BIB58) 1963; 12 Wynn (BIB54) 1956; 10 Salam (BIB44) 1998; 8 Salam (BIB43) 1996; 11 Brezinski (BIB5) 1975; 12 Graves-Morris (BIB22) 1983; 42 Brezinski (BIB7) 1978; 29 Graves-Morris, Jenkins (BIB24) 1984 Heyting (BIB32) 1927; 98 Shanks (BIB47) 1955; 34 Delahaye, Germain-Bonne (BIB18) 1982; 19 Jentschura, Mohr, Soff, Weniger (BIB34) 1999; 116 Graves-Morris, Jenkins (BIB25) 1986; 2 Cordellier (BIB15) 1984; Vol. 1071 Graves-Morris, Van Iseghem (BIB30) 1997; 90 Wynn (10.1016/S0377-0427(00)00355-1_BIB58) 1963; 12 Colton (10.1016/S0377-0427(00)00355-1_BIB12) 1983 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB24) 1984 Jentschura (10.1016/S0377-0427(00)00355-1_BIB34) 1999; 116 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB28) 1988; 23 Tan (10.1016/S0377-0427(00)00355-1_BIB49) 1988; 9 Wynn (10.1016/S0377-0427(00)00355-1_BIB55) 1961; 15 Wynn (10.1016/S0377-0427(00)00355-1_BIB56) 1961; 20 Berlekamp (10.1016/S0377-0427(00)00355-1_BIB3) 1968 Cuyt (10.1016/S0377-0427(00)00355-1_BIB17) 1987 Weniger (10.1016/S0377-0427(00)00355-1_BIB50) 1989; 10 Weniger (10.1016/S0377-0427(00)00355-1_BIB51) 1996; 246 Roberts (10.1016/S0377-0427(00)00355-1_BIB40) 1998; 8 Brezinski (10.1016/S0377-0427(00)00355-1_BIB8) 1980 Wynn (10.1016/S0377-0427(00)00355-1_BIB54) 1956; 10 Baker (10.1016/S0377-0427(00)00355-1_BIB1) 1975 Roberts (10.1016/S0377-0427(00)00355-1_BIB38) 1990; 431 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB22) 1983; 42 10.1016/S0377-0427(00)00355-1_BIB52 Salam (10.1016/S0377-0427(00)00355-1_BIB46) 1999; 97 Jones (10.1016/S0377-0427(00)00355-1_BIB36) 1980 Brezinski (10.1016/S0377-0427(00)00355-1_BIB9) 1991 McLeod (10.1016/S0377-0427(00)00355-1_BIB37) 1972; 7 10.1016/S0377-0427(00)00355-1_BIB14 10.1016/S0377-0427(00)00355-1_BIB13 10.1016/S0377-0427(00)00355-1_BIB16 Heyting (10.1016/S0377-0427(00)00355-1_BIB32) 1927; 98 Roberts (10.1016/S0377-0427(00)00355-1_BIB42) 1999; 105 Baker (10.1016/S0377-0427(00)00355-1_BIB2) 1996 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB29) 1991; 34 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB26) 1994; 51 Salam (10.1016/S0377-0427(00)00355-1_BIB45) 1998; 278 Delahaye (10.1016/S0377-0427(00)00355-1_BIB18) 1982; 19 Gutknecht (10.1016/S0377-0427(00)00355-1_BIB31) 1997; 6 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB27) 1997; 77 10.1016/S0377-0427(00)00355-1_BIB20 Graffi (10.1016/S0377-0427(00)00355-1_BIB21) 1978; 19 Roberts (10.1016/S0377-0427(00)00355-1_BIB39) 1996; 70 Salam (10.1016/S0377-0427(00)00355-1_BIB43) 1996; 11 Chandler-Wilde (10.1016/S0377-0427(00)00355-1_BIB10) 1995; 180 Brezinski (10.1016/S0377-0427(00)00355-1_BIB4) 1971; 17 Wynn (10.1016/S0377-0427(00)00355-1_BIB59) 1966; 3 Chandler-Wilde (10.1016/S0377-0427(00)00355-1_BIB11) 1998 Delahaye (10.1016/S0377-0427(00)00355-1_BIB19) 1988 Cordellier (10.1016/S0377-0427(00)00355-1_BIB15) 1984; Vol. 1071 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB30) 1997; 90 Salam (10.1016/S0377-0427(00)00355-1_BIB44) 1998; 8 Wimp (10.1016/S0377-0427(00)00355-1_BIB53) 1981 10.1016/S0377-0427(00)00355-1_BIB33 Sidi (10.1016/S0377-0427(00)00355-1_BIB48) 1986; 23 Brezinski (10.1016/S0377-0427(00)00355-1_BIB7) 1978; 29 Shanks (10.1016/S0377-0427(00)00355-1_BIB47) 1955; 34 10.1016/S0377-0427(00)00355-1_BIB35 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB23) 1997; 7 Graves-Morris (10.1016/S0377-0427(00)00355-1_BIB25) 1986; 2 Brezinski (10.1016/S0377-0427(00)00355-1_BIB5) 1975; 12 Wynn (10.1016/S0377-0427(00)00355-1_BIB57) 1962; 16 Roberts (10.1016/S0377-0427(00)00355-1_BIB41) 1998; 17 Brezinski (10.1016/S0377-0427(00)00355-1_BIB6) 1977 |
| References_xml | – year: 1996 ident: BIB2 publication-title: Padé approximants – volume: 246 start-page: 133 year: 1996 end-page: 165 ident: BIB51 article-title: A convergent, renormalised strong coupling perturbation expansion for the ground state energy of the quartic, sextic and octic anharmonic oscillator publication-title: Ann. Phys. – volume: 90 start-page: 153 year: 1997 end-page: 173 ident: BIB30 article-title: Row convergence theorems for vector-valued Padé approximants publication-title: J. Approx. Theory – volume: 34 start-page: 1 year: 1955 end-page: 42 ident: BIB47 article-title: Non-linear transformations of divergent and slowly convergent sequences publication-title: J. Math. Phys. – volume: 23 start-page: 178 year: 1986 end-page: 196 ident: BIB48 publication-title: SIAM J. Numer. Anal. – volume: 16 start-page: 301 year: 1962 end-page: 322 ident: BIB57 article-title: Acceleration techniques for iterative vector problems publication-title: Math. Comp. – volume: 7 start-page: 279 year: 1997 end-page: 294 ident: BIB23 article-title: The compass (star) identity for vector-valued rational interpolants publication-title: Adv. Comput. Math. – reference: E.J. Weniger, Prediction properties of Aitken's iterated – volume: 15 start-page: 151 year: 1961 end-page: 158 ident: BIB55 article-title: The epsilon algorithm and operational formulas of numerical analysis publication-title: Math. Comp. – reference: F. Cordellier, L’ – volume: 97 start-page: 92 year: 1999 end-page: 112 ident: BIB46 article-title: Padé-type approximants and vector Padé approximants publication-title: J. Approx. Theory – volume: 34 start-page: 315 year: 1991 end-page: 324 ident: BIB29 article-title: An extension of a row convergence theorem for vector Padé approximants publication-title: J. Comput. Appl. Math. – volume: 77 start-page: 173 year: 1997 end-page: 200 ident: BIB27 article-title: Problems and progress in vector Padé approximation publication-title: J. Comput. Appl. Math. – volume: 17 start-page: 33 year: 1998 end-page: 50 ident: BIB41 article-title: A vector Chebyshev algorithm publication-title: Numer. Algorithms – volume: 12 start-page: 273 year: 1963 end-page: 312 ident: BIB58 article-title: Continued fractions whose coefficients obey a non-commutative law of multiplication publication-title: Arch. Rational Mech. Anal. – volume: 11 start-page: 327 year: 1996 end-page: 337 ident: BIB43 article-title: An algebraic approach to the vector publication-title: Numer. Algorithms – volume: 70 start-page: 95 year: 1996 end-page: 109 ident: BIB39 article-title: On the convergence of rows of vector Padé approximants publication-title: J. Comput. Appl. Math. – volume: 2 start-page: 263 year: 1986 end-page: 289 ident: BIB25 article-title: Vector-valued rational interpolants III publication-title: Constr. Approx. – volume: 431 start-page: 285 year: 1990 end-page: 300 ident: BIB38 article-title: Clifford algebras and vector-valued rational forms I publication-title: Proc. Roy. Soc. London A – volume: 180 start-page: 705 year: 1995 end-page: 724 ident: BIB10 article-title: Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane publication-title: J. Sound Vibr. – year: 1975 ident: BIB1 publication-title: Essentials of Padé Approximants – volume: 9 start-page: 839 year: 1988 end-page: 848 ident: BIB49 article-title: Implementation of the topological epsilon algorithm publication-title: SIAM J. Sci. Statist. Comput. – volume: 8 start-page: 267 year: 1998 end-page: 289 ident: BIB44 article-title: Formal vector orthogonal polynomials publication-title: Adv. Comput. Math. – year: 1980 ident: BIB8 publication-title: Padé-Type Approximation and General Orthogonal Polynomials – volume: 105 start-page: 453 year: 1999 end-page: 466 ident: BIB42 article-title: On a representation of vector continued fractions publication-title: J. Comput. Appl. Math. – volume: 278 start-page: 147 year: 1998 end-page: 161 ident: BIB45 publication-title: What is a vector Hankel determinant? Linear Algebra Appl. – year: 1991 ident: BIB9 publication-title: Extrapolation Methods, Theory and Practice – reference: F. Cordellier, Démonstration algébrique de l'extension de l'identité de Wynn aux tables de Padé non-normales, in: L. Wuytack (Ed.), Padé Approximation and its Applications, Springer, Berlin, Lecture Notes in Mathematics, Vol. 765, 1979, pp. 36–60. – volume: 19 start-page: 1002 year: 1978 end-page: 1006 ident: BIB21 article-title: Borel summability and indeterminancy of the Stieltjes moment problem: Application to anharmonic oscillators publication-title: J. Math. Phys. – year: 1983 ident: BIB12 publication-title: Integral Equations Methods in Scattering Theory – volume: 23 start-page: 63 year: 1988 end-page: 85 ident: BIB28 article-title: Row convergence theorems for generalised inverse vector-valued Padé approximants publication-title: J. Comput. Appl. Math. – volume: Vol. 1071 start-page: 62 year: 1984 end-page: 94 ident: BIB15 article-title: Utilisation de l'invariance homographique dans les algorithmes de losange publication-title: Padé Approximation and its Applications, Bad Honnef 1983 – volume: 6 start-page: 271 year: 1997 end-page: 397 ident: BIB31 article-title: Lanczos type solvers for non-symmetric systems of linear equations publication-title: Acta Numer. – volume: 116 start-page: 28 year: 1999 end-page: 54 ident: BIB34 article-title: Convergence acceleration via combined nonlinear-condensation transformations publication-title: Comput. Phys. Comm. – reference: K. Jbilou, H. Sadok, Vector extrapolation methods, Applications and numerical comparison, this volume, J. Comput. Appl. Math. 122 (2000) 149–165. – volume: 42 start-page: 331 year: 1983 end-page: 348 ident: BIB22 article-title: Vector valued rational interpolants I publication-title: Numer. Math. – year: 1987 ident: BIB17 publication-title: Nonlinear Methods in Numerical Analysis – year: 1977 ident: BIB6 publication-title: Accélération de la Convergence en Analyse Numérique – volume: 29 start-page: 173 year: 1978 end-page: 177 ident: BIB7 article-title: Convergence acceleration of some sequences by the publication-title: Numer. Math. – volume: 98 start-page: 465 year: 1927 end-page: 490 ident: BIB32 article-title: Die Theorie der linear Gleichungen in einer Zahlenspezies mit nichtkommutatives Multiplikation publication-title: Math. Ann. – volume: 51 start-page: 205 year: 1994 end-page: 236 ident: BIB26 article-title: From matrix to vector Padé approximants publication-title: J. Comput. Appl. Math. – volume: 19 start-page: 840 year: 1982 end-page: 844 ident: BIB18 article-title: The set of logarithmically convergent sequences cannot be accelerated publication-title: SIAM J. Numer. Anal. – volume: 20 start-page: 403 year: 1961 end-page: 408 ident: BIB56 article-title: L’ publication-title: Rendi. Mat. Roma – reference: W. Gander, E.H. Golub, D. Gruntz, Solving linear systems by extrapolation in Supercomputing, Trondheim, Computer Systems Science, Vol. 62, Springer, Berlin, 1989, pp. 279–293. – volume: 8 start-page: 193 year: 1998 end-page: 219 ident: BIB40 article-title: On a vector q-d algorithm publication-title: Adv. Comput. Math. – year: 1968 ident: BIB3 publication-title: Algebraic Coding Theory – year: 1981 ident: BIB53 publication-title: Sequence Transformations and Their Applications – volume: 10 start-page: 91 year: 1956 end-page: 96 ident: BIB54 article-title: On a device for calculating the publication-title: Math. Tables Automat. Comp. – year: 1998 ident: BIB11 publication-title: A fast, two-grid method for the impedance problem in a half-plane – start-page: 144 year: 1984 end-page: 156 ident: BIB24 article-title: Generalised inverse vector-valued rational interpolation publication-title: Padé Approximation and its Applications, Vol. 1071 – year: 1980 ident: BIB36 publication-title: Continued Fractions, Encyclopedia of Mathematics and its Applications, Vol. 11 – volume: 10 start-page: 371 year: 1989 end-page: 1809 ident: BIB50 article-title: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series publication-title: Comput. Phys. Rep. – year: 1988 ident: BIB19 publication-title: Sequence Transformations – volume: 12 start-page: 317 year: 1975 end-page: 360 ident: BIB5 article-title: Généralisations de la transformation de Shanks, de la table de Padé et de l’ publication-title: Calcolo – reference: -algorithme vectoriel, interprétation géometrique et règles singulières, Exposé au Colloque d'Analyse Numérique de Gourette, 1974. – reference: process, of Wynn's epsilon algorithm and of Brezinski's iterated theta algorithm, this volume, J. Comp. Appl. Math. 122 (2000) 329–356. – reference: F. Cordellier, Thesis, University of Lille, 1989. – volume: 7 start-page: 17 year: 1972 end-page: 24 ident: BIB37 article-title: A note on the publication-title: Computing – reference: H.H.H. Homeier, Scalar Levin-type sequence transformations, this volume, J. Comput. Appl. Math. 122 (2000) 81–147. – volume: 3 start-page: 91 year: 1966 end-page: 122 ident: BIB59 article-title: On the convergence and stability of the epsilon algorithm publication-title: SIAM J. Numer. Anal. – volume: 17 start-page: 153 year: 1971 end-page: 162 ident: BIB4 article-title: Etude sur les publication-title: Numer. Math. – year: 1991 ident: 10.1016/S0377-0427(00)00355-1_BIB9 – volume: 116 start-page: 28 year: 1999 ident: 10.1016/S0377-0427(00)00355-1_BIB34 article-title: Convergence acceleration via combined nonlinear-condensation transformations publication-title: Comput. Phys. Comm. doi: 10.1016/S0010-4655(98)00111-8 – volume: 15 start-page: 151 year: 1961 ident: 10.1016/S0377-0427(00)00355-1_BIB55 article-title: The epsilon algorithm and operational formulas of numerical analysis publication-title: Math. Comp. doi: 10.1090/S0025-5718-1961-0158513-X – volume: 20 start-page: 403 year: 1961 ident: 10.1016/S0377-0427(00)00355-1_BIB56 article-title: L’ε-algoritmo e la tavola di Padé publication-title: Rendi. Mat. Roma – volume: 8 start-page: 267 year: 1998 ident: 10.1016/S0377-0427(00)00355-1_BIB44 article-title: Formal vector orthogonal polynomials publication-title: Adv. Comput. Math. doi: 10.1023/A:1018952415379 – volume: 98 start-page: 465 year: 1927 ident: 10.1016/S0377-0427(00)00355-1_BIB32 article-title: Die Theorie der linear Gleichungen in einer Zahlenspezies mit nichtkommutatives Multiplikation publication-title: Math. Ann. doi: 10.1007/BF01451604 – start-page: 144 year: 1984 ident: 10.1016/S0377-0427(00)00355-1_BIB24 article-title: Generalised inverse vector-valued rational interpolation – ident: 10.1016/S0377-0427(00)00355-1_BIB35 doi: 10.1016/S0377-0427(00)00357-5 – volume: 19 start-page: 1002 year: 1978 ident: 10.1016/S0377-0427(00)00355-1_BIB21 article-title: Borel summability and indeterminancy of the Stieltjes moment problem: Application to anharmonic oscillators publication-title: J. Math. Phys. doi: 10.1063/1.523760 – volume: 34 start-page: 1 year: 1955 ident: 10.1016/S0377-0427(00)00355-1_BIB47 article-title: Non-linear transformations of divergent and slowly convergent sequences publication-title: J. Math. Phys. doi: 10.1002/sapm19553411 – volume: 10 start-page: 371 year: 1989 ident: 10.1016/S0377-0427(00)00355-1_BIB50 article-title: Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series publication-title: Comput. Phys. Rep. doi: 10.1016/0167-7977(89)90011-7 – ident: 10.1016/S0377-0427(00)00355-1_BIB20 doi: 10.1007/978-3-642-75771-6_19 – volume: 10 start-page: 91 year: 1956 ident: 10.1016/S0377-0427(00)00355-1_BIB54 article-title: On a device for calculating the em(Sn) transformations publication-title: Math. Tables Automat. Comp. doi: 10.2307/2002183 – volume: 9 start-page: 839 year: 1988 ident: 10.1016/S0377-0427(00)00355-1_BIB49 article-title: Implementation of the topological epsilon algorithm publication-title: SIAM J. Sci. Statist. Comput. doi: 10.1137/0909056 – volume: 246 start-page: 133 year: 1996 ident: 10.1016/S0377-0427(00)00355-1_BIB51 article-title: A convergent, renormalised strong coupling perturbation expansion for the ground state energy of the quartic, sextic and octic anharmonic oscillator publication-title: Ann. Phys. doi: 10.1006/aphy.1996.0023 – year: 1981 ident: 10.1016/S0377-0427(00)00355-1_BIB53 – volume: 278 start-page: 147 year: 1998 ident: 10.1016/S0377-0427(00)00355-1_BIB45 publication-title: What is a vector Hankel determinant? Linear Algebra Appl. doi: 10.1016/S0024-3795(97)10091-X – volume: 16 start-page: 301 year: 1962 ident: 10.1016/S0377-0427(00)00355-1_BIB57 article-title: Acceleration techniques for iterative vector problems publication-title: Math. Comp. doi: 10.1090/S0025-5718-1962-0145647-X – year: 1998 ident: 10.1016/S0377-0427(00)00355-1_BIB11 – volume: 23 start-page: 63 year: 1988 ident: 10.1016/S0377-0427(00)00355-1_BIB28 article-title: Row convergence theorems for generalised inverse vector-valued Padé approximants publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(88)90331-7 – volume: 77 start-page: 173 year: 1997 ident: 10.1016/S0377-0427(00)00355-1_BIB27 article-title: Problems and progress in vector Padé approximation publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(96)00127-6 – year: 1988 ident: 10.1016/S0377-0427(00)00355-1_BIB19 – volume: 34 start-page: 315 year: 1991 ident: 10.1016/S0377-0427(00)00355-1_BIB29 article-title: An extension of a row convergence theorem for vector Padé approximants publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(91)90092-X – volume: 7 start-page: 279 year: 1997 ident: 10.1016/S0377-0427(00)00355-1_BIB23 article-title: The compass (star) identity for vector-valued rational interpolants publication-title: Adv. Comput. Math. doi: 10.1023/A:1018951020406 – ident: 10.1016/S0377-0427(00)00355-1_BIB16 – volume: 431 start-page: 285 year: 1990 ident: 10.1016/S0377-0427(00)00355-1_BIB38 article-title: Clifford algebras and vector-valued rational forms I publication-title: Proc. Roy. Soc. London A doi: 10.1098/rspa.1990.0131 – volume: 180 start-page: 705 year: 1995 ident: 10.1016/S0377-0427(00)00355-1_BIB10 article-title: Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane publication-title: J. Sound Vibr. doi: 10.1006/jsvi.1995.0110 – ident: 10.1016/S0377-0427(00)00355-1_BIB33 doi: 10.1016/S0377-0427(00)00359-9 – volume: 105 start-page: 453 year: 1999 ident: 10.1016/S0377-0427(00)00355-1_BIB42 article-title: On a representation of vector continued fractions publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(99)00034-5 – year: 1983 ident: 10.1016/S0377-0427(00)00355-1_BIB12 – volume: 12 start-page: 273 year: 1963 ident: 10.1016/S0377-0427(00)00355-1_BIB58 article-title: Continued fractions whose coefficients obey a non-commutative law of multiplication publication-title: Arch. Rational Mech. Anal. doi: 10.1007/BF00281229 – volume: 17 start-page: 33 year: 1998 ident: 10.1016/S0377-0427(00)00355-1_BIB41 article-title: A vector Chebyshev algorithm publication-title: Numer. Algorithms doi: 10.1023/A:1011633327892 – volume: 42 start-page: 331 year: 1983 ident: 10.1016/S0377-0427(00)00355-1_BIB22 article-title: Vector valued rational interpolants I publication-title: Numer. Math. doi: 10.1007/BF01389578 – year: 1977 ident: 10.1016/S0377-0427(00)00355-1_BIB6 – volume: 2 start-page: 263 year: 1986 ident: 10.1016/S0377-0427(00)00355-1_BIB25 article-title: Vector-valued rational interpolants III publication-title: Constr. Approx. doi: 10.1007/BF01893432 – volume: 51 start-page: 205 year: 1994 ident: 10.1016/S0377-0427(00)00355-1_BIB26 article-title: From matrix to vector Padé approximants publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(92)00008-W – year: 1996 ident: 10.1016/S0377-0427(00)00355-1_BIB2 – volume: 6 start-page: 271 year: 1997 ident: 10.1016/S0377-0427(00)00355-1_BIB31 article-title: Lanczos type solvers for non-symmetric systems of linear equations publication-title: Acta Numer. doi: 10.1017/S0962492900002737 – ident: 10.1016/S0377-0427(00)00355-1_BIB14 doi: 10.1007/BFb0085574 – volume: 70 start-page: 95 year: 1996 ident: 10.1016/S0377-0427(00)00355-1_BIB39 article-title: On the convergence of rows of vector Padé approximants publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(95)00133-6 – volume: 90 start-page: 153 year: 1997 ident: 10.1016/S0377-0427(00)00355-1_BIB30 article-title: Row convergence theorems for vector-valued Padé approximants publication-title: J. Approx. Theory doi: 10.1006/jath.1996.3077 – year: 1980 ident: 10.1016/S0377-0427(00)00355-1_BIB36 – ident: 10.1016/S0377-0427(00)00355-1_BIB13 – ident: 10.1016/S0377-0427(00)00355-1_BIB52 doi: 10.1016/S0377-0427(00)00363-0 – year: 1987 ident: 10.1016/S0377-0427(00)00355-1_BIB17 – volume: 3 start-page: 91 year: 1966 ident: 10.1016/S0377-0427(00)00355-1_BIB59 article-title: On the convergence and stability of the epsilon algorithm publication-title: SIAM J. Numer. Anal. doi: 10.1137/0703007 – volume: 8 start-page: 193 year: 1998 ident: 10.1016/S0377-0427(00)00355-1_BIB40 article-title: On a vector q-d algorithm publication-title: Adv. Comput. Math. doi: 10.1023/A:1018944213562 – volume: Vol. 1071 start-page: 62 year: 1984 ident: 10.1016/S0377-0427(00)00355-1_BIB15 article-title: Utilisation de l'invariance homographique dans les algorithmes de losange – volume: 11 start-page: 327 year: 1996 ident: 10.1016/S0377-0427(00)00355-1_BIB43 article-title: An algebraic approach to the vector ε-algorithm publication-title: Numer. Algorithms doi: 10.1007/BF02142505 – volume: 19 start-page: 840 year: 1982 ident: 10.1016/S0377-0427(00)00355-1_BIB18 article-title: The set of logarithmically convergent sequences cannot be accelerated publication-title: SIAM J. Numer. Anal. doi: 10.1137/0719059 – volume: 97 start-page: 92 year: 1999 ident: 10.1016/S0377-0427(00)00355-1_BIB46 article-title: Padé-type approximants and vector Padé approximants publication-title: J. Approx. Theory doi: 10.1006/jath.1997.3263 – year: 1980 ident: 10.1016/S0377-0427(00)00355-1_BIB8 – year: 1975 ident: 10.1016/S0377-0427(00)00355-1_BIB1 – volume: 12 start-page: 317 year: 1975 ident: 10.1016/S0377-0427(00)00355-1_BIB5 article-title: Généralisations de la transformation de Shanks, de la table de Padé et de l’ε-algorithme publication-title: Calcolo doi: 10.1007/BF02575753 – volume: 29 start-page: 173 year: 1978 ident: 10.1016/S0377-0427(00)00355-1_BIB7 article-title: Convergence acceleration of some sequences by the ε-algorithm publication-title: Numer. Math. doi: 10.1007/BF01390336 – volume: 17 start-page: 153 year: 1971 ident: 10.1016/S0377-0427(00)00355-1_BIB4 article-title: Etude sur les ε-et ρ-algorithmes publication-title: Numer. Math. doi: 10.1007/BF01406003 – volume: 23 start-page: 178 year: 1986 ident: 10.1016/S0377-0427(00)00355-1_BIB48 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0723013 – volume: 7 start-page: 17 year: 1972 ident: 10.1016/S0377-0427(00)00355-1_BIB37 article-title: A note on the ε-algorithm publication-title: Computing doi: 10.1007/BF02279938 – year: 1968 ident: 10.1016/S0377-0427(00)00355-1_BIB3 |
| SSID | ssj0006914 |
| Score | 1.8291032 |
| Snippet | The epsilon algorithm is recommended as the best
all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 51 |
| SubjectTerms | Compass identity Cross rule Designant Epsilon algorithm Padé qd algorithm Star identity Vector-valued approximant Wynn |
| Title | The epsilon algorithm and related topics |
| URI | https://dx.doi.org/10.1016/S0377-0427(00)00355-1 |
| Volume | 122 |
| WOSCitedRecordID | wos000089756400005&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: ScienceDirect Freedom Collection - Elsevier customDbUrl: eissn: 1879-1778 dateEnd: 20180131 omitProxy: false ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: AIEXJ dateStart: 19950220 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1La9wwEBYlyaE9lD5SmqYtPvSQHORKsiVZx6VsHyEJIVnK3owtyU1g6112tyE_vyNLllM2pA_oxRghWdjzMfNpPA-E3pE8t2A4hfMBMJzLxmI4BlW4kaTijTMZXdO-r8fy9LSYTtVZCCtade0EZNsWNzdq8V9FDWMgbJc6-xfijg-FAbgHocMVxA7XPxa8XayuZi7OePZtDqf_S98Ho8tbAYK5ni_6GPdNWqq7Ng-9i7Ar5RqI6vdY4TXy8E-uedEKn8yXS1-r4Cw9T4d_OC5o29P0dByHL6oAwlH6i8uBxOC14AfbyIXx-VdSYte5w1sWr04LqTCVvklP1LeMbQDLa89QejbYYXKnhvfOhou4G_Bw187aOWQ5x3QwazHYsJvrppLuv6nLt99mkivQgdujL-PpUbTcQvla8P2zh4yv98OGB4Qchs3u5jK3-MnkCXocJJiMPCCeoge2fYYenQwye44OABpJgEYSoZGAjJMAjcRDYxdNPo4nHz7j0CkDa9DRa2xpzjRVteCm0A0XlrLG8lrpTBnLWWFonROjObd1Y01DrCTK5kLISlQ6q7MXaKudt_YlSoyoGkYtEFcDE0xVwHGeMeDQgtamytQeyvtXLnWoIu-amczKIVwwc-Xj4UuVpCs9y3lJ91Aaly18GZXfLSj671kGLug5XglAuH_pq39fuo8eDnh_jbbWyx_2DdrR1-ur1fJtgMtPSsp5rw |
| 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=The+epsilon+algorithm+and+related+topics&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Graves-Morris%2C+P.R.&rft.au=Roberts%2C+D.E.&rft.au=Salam%2C+A.&rft.date=2000-10-01&rft.pub=Elsevier+B.V&rft.issn=0377-0427&rft.eissn=1879-1778&rft.volume=122&rft.issue=1&rft.spage=51&rft.epage=80&rft_id=info:doi/10.1016%2FS0377-0427%2800%2900355-1&rft.externalDocID=S0377042700003551 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |