A generalization of the G-transformation and the related algorithms
In this paper, a generalization of the G-transformation is proposed together with the corresponding auxiliary rs-algorithm for implementation. We show that the related generalization of the rs-algorithm is equivalent to a generalized qd-algorithm. Applications of the generalization of the G-transfor...
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| Veröffentlicht in: | Applied numerical mathematics Jg. 60; H. 12; S. 1221 - 1230 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier B.V
01.12.2010
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| ISSN: | 0168-9274, 1873-5460 |
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| Abstract | In this paper, a generalization of the
G-transformation is proposed together with the corresponding auxiliary
rs-algorithm for implementation. We show that the related generalization of the
rs-algorithm is equivalent to a generalized
qd-algorithm. Applications of the generalization of the
G-transformation to the computation of infinite integrals are also given. |
|---|---|
| AbstractList | In this paper, a generalization of the
G-transformation is proposed together with the corresponding auxiliary
rs-algorithm for implementation. We show that the related generalization of the
rs-algorithm is equivalent to a generalized
qd-algorithm. Applications of the generalization of the
G-transformation to the computation of infinite integrals are also given. In this paper, a generalization of the G-transformation is proposed together with the corresponding auxiliary rs-algorithm for implementation. We show that the related generalization of the rs-algorithm is equivalent to a generalized qd-algorithm. Applications of the generalization of the G-transformation to the computation of infinite integrals are also given. |
| Author | He, Yi Sun, Jian-Qing Hu, Xing-Biao Brezinski, Claude |
| Author_xml | – sequence: 1 givenname: Claude surname: Brezinski fullname: Brezinski, Claude email: Claude.Brezinski@univ-lille1.fr organization: Laboratoire Paul Painlevé, UMR CNRS 8524, UFR de Mathématiques Pures et Appliquées, Université des Sciences et Technologies de Lille, 59655-Villeneuve d'Ascq cedex, France – sequence: 2 givenname: Yi surname: He fullname: He, Yi email: heyi@lsec.cc.ac.cn organization: LSEC, Institute of Computational Mathematics and Scientific, Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China – sequence: 3 givenname: Xing-Biao surname: Hu fullname: Hu, Xing-Biao email: hxb@lsec.cc.ac.cn organization: LSEC, Institute of Computational Mathematics and Scientific, Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China – sequence: 4 givenname: Jian-Qing surname: Sun fullname: Sun, Jian-Qing email: sunjq@lsec.cc.ac.cn organization: LSEC, Institute of Computational Mathematics and Scientific, Engineering Computing, AMSS, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China |
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| Cites_doi | 10.1007/BF01396314 10.1007/BF01600331 10.1137/0708037 10.1137/0704032 10.1007/BF01399010 10.1137/0710001 |
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| Keywords | rs-algorithm G-transformation qd-algorithm G-algorithm |
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| References | Delahaye, Germain-Bonne (br0030) 1980; 35 Brezinski (br0010) 1980; 35 Brezinski, Redivo Zaglia (br0020) 1991 Henrici (br0060) 1974 Nakamura (br0070) 2000 Salam (br0110) 1991; 34 Gray, Atchison (br0040) 1967; 4 Rutishauser (br0090) 1954; 5 Rutishauser (br0100) 1958; 49 Pye, Atchison (br0080) 1973; 10 Gray, Atchison, McWilliams (br0050) 1971; 8 Wynn (br0120) 1956; 10 Gray (10.1016/j.apnum.2010.03.008_br0050) 1971; 8 Henrici (10.1016/j.apnum.2010.03.008_br0060) 1974 Brezinski (10.1016/j.apnum.2010.03.008_br0010) 1980; 35 Salam (10.1016/j.apnum.2010.03.008_br0110) 1991; 34 Brezinski (10.1016/j.apnum.2010.03.008_br0020) 1991 Pye (10.1016/j.apnum.2010.03.008_br0080) 1973; 10 Nakamura (10.1016/j.apnum.2010.03.008_br0070) 2000 Rutishauser (10.1016/j.apnum.2010.03.008_br0100) 1958; 49 Wynn (10.1016/j.apnum.2010.03.008_br0120) 1956; 10 Rutishauser (10.1016/j.apnum.2010.03.008_br0090) 1954; 5 Gray (10.1016/j.apnum.2010.03.008_br0040) 1967; 4 Delahaye (10.1016/j.apnum.2010.03.008_br0030) 1980; 35 |
| References_xml | – volume: 35 start-page: 443 year: 1980 end-page: 457 ident: br0030 article-title: Résultats négatifs en accélération de la convergence publication-title: Numer. Math. – volume: 10 start-page: 1 year: 1973 end-page: 7 ident: br0080 article-title: An algorithm for the computation of the higher order publication-title: SIAM J. Numer. Anal. – volume: 49 start-page: 47 year: 1958 end-page: 81 ident: br0100 article-title: Solution of eigenvalue problems with the LR-transformation publication-title: Nat. Bur. Standards Appl. Math. Ser. – year: 1974 ident: br0060 article-title: Applied and Computational Complex Analysis, Vol. 1 – volume: 34 start-page: 455 year: 1991 end-page: 464 ident: br0110 article-title: On a generalization of the publication-title: J. Comput. Appl. Math. – volume: 10 start-page: 91 year: 1956 end-page: 96 ident: br0120 article-title: On a device for computing the publication-title: MTAC – volume: 4 start-page: 363 year: 1967 end-page: 371 ident: br0040 article-title: Nonlinear transformations related to the evaluation of improper integrals. I publication-title: SIAM J. Numer. Anal. – volume: 8 start-page: 365 year: 1971 end-page: 381 ident: br0050 article-title: Higher order publication-title: SIAM J. Numer. Anal. – volume: 35 start-page: 175 year: 1980 end-page: 187 ident: br0010 article-title: A general extrapolation algorithm publication-title: Numer. Math. – year: 1991 ident: br0020 article-title: Extrapolation Methods. Theory and Practice – start-page: 189 year: 2000 end-page: 200 ident: br0070 publication-title: Applied Integrable Systems – volume: 5 start-page: 233 year: 1954 end-page: 251 ident: br0090 article-title: Der Quotienten-Differenzen-Algorithmus publication-title: Z. Angew. Math. Phys. – volume: 49 start-page: 47 year: 1958 ident: 10.1016/j.apnum.2010.03.008_br0100 article-title: Solution of eigenvalue problems with the LR-transformation publication-title: Nat. Bur. Standards Appl. Math. Ser. – volume: 35 start-page: 175 year: 1980 ident: 10.1016/j.apnum.2010.03.008_br0010 article-title: A general extrapolation algorithm publication-title: Numer. Math. doi: 10.1007/BF01396314 – year: 1991 ident: 10.1016/j.apnum.2010.03.008_br0020 – volume: 5 start-page: 233 year: 1954 ident: 10.1016/j.apnum.2010.03.008_br0090 article-title: Der Quotienten-Differenzen-Algorithmus publication-title: Z. Angew. Math. Phys. doi: 10.1007/BF01600331 – volume: 8 start-page: 365 year: 1971 ident: 10.1016/j.apnum.2010.03.008_br0050 article-title: Higher order G-transformations publication-title: SIAM J. Numer. Anal. doi: 10.1137/0708037 – volume: 4 start-page: 363 year: 1967 ident: 10.1016/j.apnum.2010.03.008_br0040 article-title: Nonlinear transformations related to the evaluation of improper integrals. I publication-title: SIAM J. Numer. Anal. doi: 10.1137/0704032 – volume: 34 start-page: 455 year: 1991 ident: 10.1016/j.apnum.2010.03.008_br0110 article-title: On a generalization of the ε-algorithm publication-title: J. Comput. Appl. Math. – volume: 10 start-page: 91 year: 1956 ident: 10.1016/j.apnum.2010.03.008_br0120 article-title: On a device for computing the em(Sn) transformation publication-title: MTAC – volume: 35 start-page: 443 year: 1980 ident: 10.1016/j.apnum.2010.03.008_br0030 article-title: Résultats négatifs en accélération de la convergence publication-title: Numer. Math. doi: 10.1007/BF01399010 – start-page: 189 year: 2000 ident: 10.1016/j.apnum.2010.03.008_br0070 – volume: 10 start-page: 1 year: 1973 ident: 10.1016/j.apnum.2010.03.008_br0080 article-title: An algorithm for the computation of the higher order G-transformation publication-title: SIAM J. Numer. Anal. doi: 10.1137/0710001 – year: 1974 ident: 10.1016/j.apnum.2010.03.008_br0060 |
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G-transformation is proposed together with the corresponding auxiliary
rs-algorithm for implementation. We show that the... In this paper, a generalization of the G-transformation is proposed together with the corresponding auxiliary rs-algorithm for implementation. We show that the... |
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| SubjectTerms | Algorithms Computation Equivalence G-algorithm G-transformation Infinite integrals Mathematical models qd-algorithm rs-algorithm |
| Title | A generalization of the G-transformation and the related algorithms |
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