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Volumn 20, Issue 3, 1996, Pages 299-318

Extrapolation algorithms and Padé approximations: A historical survey

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; POLYNOMIALS;

EID: 0030103537     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/0168-9274(95)00110-7     Document Type: Article
Times cited : (93)

References (138)
  • 2
    • 0000665315 scopus 로고
    • On Bernoulli's numerical solution of algebraic equations
    • A.C. Aitken, On Bernoulli's numerical solution of algebraic equations, Proc. R. Soc. Edinb. 46 (1926) 289-305.
    • (1926) Proc. R. Soc. Edinb. , vol.46 , pp. 289-305
    • Aitken, A.C.1
  • 3
    • 0005282024 scopus 로고
    • Interpolation
    • J. Molk, ed., Tome I, Fasc. 1, 1-21 (Gauthier-Villars, Paris, 1904-1912) reprinted by Editions Gabay, Paris
    • H. Andoyer, Interpolation, in: J. Molk, ed., Encyclopédie des Sciences Mathématiques Pures et Appliquées, Tome I, vol. 4, Fasc. 1, 1-21 (Gauthier-Villars, Paris, 1904-1912) 127-160; reprinted by (Editions Gabay, Paris, 1993).
    • (1993) Encyclopédie des Sciences Mathématiques Pures et Appliquées , vol.4 , pp. 127-160
    • Andoyer, H.1
  • 4
    • 0001325525 scopus 로고
    • Application of the Padé method to the investigation of some magnetic properties of the Ising model
    • G.A. Baker Jr, Application of the Padé method to the investigation of some magnetic properties of the Ising model, Phys. Rev. 124 (1961) 768-774.
    • (1961) Phys. Rev. , vol.124 , pp. 768-774
    • Baker G.A., Jr.1
  • 5
    • 0004160175 scopus 로고    scopus 로고
    • 2 vols. (Addison-Wesley, Reading, MA, 1981); also: Cambridge University Press, Cambridge, 2nd ed.
    • G.A. Baker Jr and P.R. Graves-Morris, Padé Approximates, 2 vols. (Addison-Wesley, Reading, MA, 1981); also: (Cambridge University Press, Cambridge, 2nd ed., 1996).
    • (1996) Padé Approximates
    • Baker G.A., Jr.1    Graves-Morris, P.R.2
  • 6
    • 0005281367 scopus 로고
    • La méthode d'intégration numérique de romberg
    • Librairie Universitaire, Louvain
    • F.L. Bauer, La méthode d'intégration numérique de Romberg, in: Colloque sur l'Analyse Numérique (Librairie Universitaire, Louvain, 1961) 119-129.
    • (1961) Colloque sur l'Analyse Numérique , pp. 119-129
    • Bauer, F.L.1
  • 7
    • 0005385514 scopus 로고
    • A connection between the E-algorithm and the epsilon-algorithm
    • C. Brezinski, ed., Baltzer, Basel
    • B. Beckermann, A connection between the E-algorithm and the epsilon-algorithm, in: C. Brezinski, ed., Numerical and Applied Mathematics (Baltzer, Basel, 1989) 443-446.
    • (1989) Numerical and Applied Mathematics , pp. 443-446
    • Beckermann, B.1
  • 9
    • 0022118375 scopus 로고
    • Sequence transformations as statistical tools
    • A. Berlinet, Sequence transformations as statistical tools, Appl. Numer. Math. 1 (1985) 531-544.
    • (1985) Appl. Numer. Math. , vol.1 , pp. 531-544
    • Berlinet, A.1
  • 10
    • 0005280127 scopus 로고
    • On Rayleigh's principle in the theory of differential equations of mathematical physics and upon Euler's method in the calculus of variation
    • in Russian
    • N. Bogolyubov, N. Krylov, On Rayleigh's principle in the theory of differential equations of mathematical physics and upon Euler's method in the calculus of variation, Acad. Sci. Ukraine (Phys. Math.) 3 (1926) 3-22 (in Russian).
    • (1926) Acad. Sci. Ukraine (Phys. Math.) , vol.3 , pp. 3-22
    • Bogolyubov, N.1    Krylov, N.2
  • 11
    • 84971114256 scopus 로고
    • Eigenvalues of differential equations by finite-difference methods
    • H.C. Bolton, H.I. Scoins, Eigenvalues of differential equations by finite-difference methods, Proc. Cambridge Phil. Soc. 52 (1956) 215-229.
    • (1956) Proc. Cambridge Phil. Soc. , vol.52 , pp. 215-229
    • Bolton, H.C.1    Scoins, H.I.2
  • 12
    • 0005323285 scopus 로고
    • Application de l'ε-algorithme à la résolution des systèmes non linéaires
    • C. Brezinski, Application de l'ε-algorithme à la résolution des systèmes non linéaires, C. R. Acad. Sci. Paris 271 A (1970) 1174-1177.
    • (1970) C. R. Acad. Sci. Paris , vol.271 A , pp. 1174-1177
    • Brezinski, C.1
  • 13
    • 0000701158 scopus 로고
    • Accélération de suites à convergence logarithmique
    • C. Brezinski, Accélération de suites à convergence logarithmique, C. R. Acad. Sci. Paris 273 A (1971) 727-730.
    • (1971) C. R. Acad. Sci. Paris , vol.273 A , pp. 727-730
    • Brezinski, C.1
  • 14
    • 51249190243 scopus 로고
    • Généralisation de la transformation de shanks, de la table de padé et de l'ε-algorithme
    • C. Brezinski, Généralisation de la transformation de Shanks, de la table de Padé et de l'ε-algorithme, Calcolo 12 (1975) 317-360.
    • (1975) Calcolo , vol.12 , pp. 317-360
    • Brezinski, C.1
  • 15
    • 0000172225 scopus 로고
    • A general extrapolation algorithm
    • C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980) 175-187.
    • (1980) Numer. Math. , vol.35 , pp. 175-187
    • Brezinski, C.1
  • 17
    • 0005280873 scopus 로고
    • Error control in convergence acceleration processes
    • C. Brezinski, Error control in convergence acceleration processes, IMA J. Numer. Anal. 3 (1983) 65-80.
    • (1983) IMA J. Numer. Anal. , vol.3 , pp. 65-80
    • Brezinski, C.1
  • 18
    • 0005321633 scopus 로고
    • Composite sequence transformations
    • C. Brezinski, Composite sequence transformations, Numer. Math. 46 (1985) 311-321.
    • (1985) Numer. Math. , vol.46 , pp. 311-321
    • Brezinski, C.1
  • 19
    • 0005282025 scopus 로고
    • A new approach to convergence acceleration methods
    • A. Cuyt, ed., Reidel, Dordrecht
    • C. Brezinski, A new approach to convergence acceleration methods, in: A. Cuyt, ed., Nonlinear Numerical Methods and Rational Approximation (Reidel, Dordrecht, 1988) 373-405.
    • (1988) Nonlinear Numerical Methods and Rational Approximation , pp. 373-405
    • Brezinski, C.1
  • 20
    • 0002481251 scopus 로고
    • Quasi-linear extrapolation processes
    • R.P. Agarwal et al., eds., Singapore 1988, ISNM 86 Birkhäuser, Basel
    • C. Brezinski, Quasi-linear extrapolation processes, in: R.P. Agarwal et al., eds., Numerical Mathematics. Singapore 1988, ISNM 86 (Birkhäuser, Basel, 1988) 61-78.
    • (1988) Numerical Mathematics , pp. 61-78
    • Brezinski, C.1
  • 21
    • 0005342476 scopus 로고
    • A survey of iterative extrapolation by the E-algorithm
    • C. Brezinski, A survey of iterative extrapolation by the E-algorithm, Det Kong. Norske Vid. Selsk. Skr. 2 (1989) 1-26.
    • (1989) Det Kong. Norske Vid. Selsk. Skr. , vol.2 , pp. 1-26
    • Brezinski, C.1
  • 25
    • 0005388342 scopus 로고
    • The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer
    • C. Brezinski, The generalizations of Newton's interpolation formula due to Mühlbach and Andoyer, Elect. Trans. Numer. Anal. 2 (1994) 130-137.
    • (1994) Elect. Trans. Numer. Anal. , vol.2 , pp. 130-137
    • Brezinski, C.1
  • 26
    • 0020988251 scopus 로고
    • Convergence acceleration by extraction of linear subsequences
    • C. Brezinski, J.P. Delahaye and B. Germain-Bonne, Convergence acceleration by extraction of linear subsequences, SIAM J. Numer. Anal. 20 (1983) 1099-1105.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 1099-1105
    • Brezinski, C.1    Delahaye, J.P.2    Germain-Bonne, B.3
  • 27
    • 84976066915 scopus 로고    scopus 로고
    • A derivation of extrapolation algorithms based on error estimates
    • to appear
    • C. Brezinski and A.C. Matos, A derivation of extrapolation algorithms based on error estimates, J. Comput. Appl. Math., to appear.
    • J. Comput. Appl. Math.
    • Brezinski, C.1    Matos, A.C.2
  • 28
    • 0005344839 scopus 로고
    • Construction of extrapolation processes
    • C. Brezinski and M. Redivo Zaglia, Construction of extrapolation processes, Appl. Numer. Math. 8 (1991) 11-23.
    • (1991) Appl. Numer. Math. , vol.8 , pp. 11-23
    • Brezinski, C.1    Zaglia, M.R.2
  • 30
    • 0003030455 scopus 로고
    • Treatment of near-breakdown in the CGS algorithm
    • C. Brezinski and M. Redivo Zaglia, Treatment of near-breakdown in the CGS algorithm, Numerical Algor. 7 (1994) 33-73.
    • (1994) Numerical Algor. , vol.7 , pp. 33-73
    • Brezinski, C.1    Zaglia, M.R.2
  • 31
    • 51249165521 scopus 로고
    • A general extrapolation procedure revisited
    • C. Brezinski and M. Redivo Zaglia, A general extrapolation procedure revisited, Adv. Comput. Math. 2 (1994) 461-477.
    • (1994) Adv. Comput. Math. , vol.2 , pp. 461-477
    • Brezinski, C.1    Zaglia, M.R.2
  • 32
    • 0001595068 scopus 로고
    • Avoiding breakdown and near-breakdown in Lanczos type algorithms
    • C. Brezinski, M. Redivo Zaglia and H. Sadok, Avoiding breakdown and near-breakdown in Lanczos type algorithms, Numerical Algor. 1 (1991) 261-274.
    • (1991) Numerical Algor. , vol.1 , pp. 261-274
    • Brezinski, C.1    Zaglia, M.R.2    Sadok, H.3
  • 33
    • 21144473062 scopus 로고
    • A breakdown-free Lanczos type algorithm for solving linear systems
    • C. Brezinski, M. Redivo Zaglia and H. Sadok, A breakdown-free Lanczos type algorithm for solving linear systems, Numer. Math. 63 (1992) 29-38.
    • (1992) Numer. Math. , vol.63 , pp. 29-38
    • Brezinski, C.1    Zaglia, M.R.2    Sadok, H.3
  • 34
    • 84966212531 scopus 로고
    • The solution of systems of equations using the vector ε-algorithm, and an application to boundary value problems
    • C. Brezinski and A.C. Rieu, The solution of systems of equations using the vector ε-algorithm, and an application to boundary value problems, Math. Comp. 28 (1974) 731-741.
    • (1974) Math. Comp. , vol.28 , pp. 731-741
    • Brezinski, C.1    Rieu, A.C.2
  • 35
    • 70350315109 scopus 로고
    • Padé approximations
    • P.G. Ciarlet and J.L. Lions, eds., North-Holland, Amsterdam
    • C. Brezinski and J. van Iseghem, Padé approximations, in: P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Analysis, Vol. III (North-Holland, Amsterdam, 1994) 47-222.
    • (1994) Handbook of Numerical Analysis , vol.3 , pp. 47-222
    • Brezinski, C.1    Van Iseghem, J.2
  • 36
    • 0005364357 scopus 로고
    • Sequences of transformations and triangular recursion schemes with applications in numerical analysis
    • C. Brezinski and G. Walz, Sequences of transformations and triangular recursion schemes with applications in numerical analysis, J. Comput. Appl. Math. 34 (1991) 361-383.
    • (1991) J. Comput. Appl. Math. , vol.34 , pp. 361-383
    • Brezinski, C.1    Walz, G.2
  • 37
    • 27844591085 scopus 로고
    • Numerical treatment of ordinary differential equations by extrapolation methods
    • R. Bulirsch and J. Stoer, Numerical treatment of ordinary differential equations by extrapolation methods, Numer. Math. 8 (1966) 1-13.
    • (1966) Numer. Math. , vol.8 , pp. 1-13
    • Bulirsch, R.1    Stoer, J.2
  • 39
    • 0039941908 scopus 로고
    • Ein beitrag zur mannigfaltigkeitslehre
    • G. Cantor, Ein Beitrag zur Mannigfaltigkeitslehre, J. Reine Angew. Math. 84 (1878) 242-258.
    • (1878) J. Reine Angew. Math. , vol.84 , pp. 242-258
    • Cantor, G.1
  • 40
    • 0005346312 scopus 로고
    • On a general epsilon algorithm
    • C. Brezinski, ed., Baltzer, Basel
    • C. Carstensen, On a general epsilon algorithm, in: C. Brezinski, ed., Numerical and Applied Mathematics (Baltzer, Basel, 1989) 437-441.
    • (1989) Numerical and Applied Mathematics , pp. 437-441
    • Carstensen, C.1
  • 43
    • 0002135374 scopus 로고
    • Démonstration algébrique de l'extension de l'identité de wynn aux tables de padé non normales
    • L. Wuytack, ed., Lecture Notes in Mathematics Springer, Berlin
    • 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, Lecture Notes in Mathematics 765 (Springer, Berlin, 1979) 36-60.
    • (1979) Padé Approximation and its Applications , vol.765 , pp. 36-60
    • Cordellier, F.1
  • 45
    • 84966218562 scopus 로고
    • Automatic selection of sequence transformations
    • J.P. Delahaye, Automatic selection of sequence transformations, Math. Comp. 37 (1981) 197-204.
    • (1981) Math. Comp. , vol.37 , pp. 197-204
    • Delahaye, J.P.1
  • 47
    • 0001296647 scopus 로고
    • Résultats négatifs en accélération de la convergence
    • J.P. Delahaye and B. Germain-Bonne, Résultats négatifs en accélération de la convergence, Numer. Math. 35 (1980) 443-457.
    • (1980) Numer. Math. , vol.35 , pp. 443-457
    • Delahaye, J.P.1    Germain-Bonne, B.2
  • 50
    • 0005282027 scopus 로고
    • Richardson-extrapolation and Romberg-integration
    • J. Dutka, Richardson-extrapolation and Romberg-integration, Historia Math. 11 (1984) 3-21.
    • (1984) Historia Math. , vol.11 , pp. 3-21
    • Dutka, J.1
  • 52
    • 0023427925 scopus 로고
    • An algorithm for a generalization of the Richardson extrapolation process
    • W.F. Ford and A. Sidi, An algorithm for a generalization of the Richardson extrapolation process, SIAM J. Numer. Anal. 24 (1987) 1212-1232.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1212-1232
    • Ford, W.F.1    Sidi, A.2
  • 53
    • 84966252930 scopus 로고
    • On the solution of systems of equations by the epsilon algorithm of Wynn
    • E. Gekeler, On the solution of systems of equations by the epsilon algorithm of Wynn, Math. Comp. 26 (1972) 427-436.
    • (1972) Math. Comp. , vol.26 , pp. 427-436
    • Gekeler, E.1
  • 56
    • 0001505099 scopus 로고
    • On extrapolation algorithms for initial-value problems
    • W.B. Gragg, On extrapolation algorithms for initial-value problems, SIAM J. Numer. Anal. 2 (1965) 384-403.
    • (1965) SIAM J. Numer. Anal. , vol.2 , pp. 384-403
    • Gragg, W.B.1
  • 57
    • 0000996745 scopus 로고
    • Vector valued rational interpolants I
    • P.R. Graves-Morris, Vector valued rational interpolants I, Numer. Math. 42 (1983) 331-348.
    • (1983) Numer. Math. , vol.42 , pp. 331-348
    • Graves-Morris, P.R.1
  • 59
    • 0003219224 scopus 로고
    • The unsymmetric Lanczos algorithms and their relations to Padé approximation, continued fractions, and the qd algorithm
    • M.H. Gutknecht, The unsymmetric Lanczos algorithms and their relations to Padé approximation, continued fractions, and the qd algorithm, in: Proceedings of the Copper Mountain Conference on Iterative Methods (1990).
    • (1990) Proceedings of the Copper Mountain Conference on Iterative Methods
    • Gutknecht, M.H.1
  • 60
    • 0018732881 scopus 로고
    • Generalized Neville type extrapolation schemes
    • T. Håvie, Generalized Neville type extrapolation schemes, BIT 19 (1979) 204-213.
    • (1979) BIT , vol.19 , pp. 204-213
    • Håvie, T.1
  • 64
    • 0002270759 scopus 로고
    • Sur la fonction exponentielle
    • C. Hermite, Sur la fonction exponentielle, C. R. Acad. Sci. Paris 77 (1873) 18-24, 74-79, 226-233, 285-293.
    • (1873) C. R. Acad. Sci. Paris , vol.77 , pp. 18-24
    • Hermite, C.1
  • 65
    • 85029986597 scopus 로고
    • De circuli magnitudine inventa
    • C. Huygens, De circuli magnitudine inventa, in: Œuvres, t. XII (1654).
    • (1654) ŒUvres , vol.12
    • Huygens, C.1
  • 66
    • 84941613911 scopus 로고
    • Über die darstellung einer reihe gegebener werthe durch eine gebrochen rationale funktion
    • C.G.J. Jacobi, Über die Darstellung einer Reihe gegebener Werthe durch eine gebrochen rationale Funktion, J. Reine Angew. Math. 30 (1845) 127-156.
    • (1845) J. Reine Angew. Math. , vol.30 , pp. 127-156
    • Jacobi, C.G.J.1
  • 67
    • 0001003956 scopus 로고
    • Some results about vector extrapolation methods and related fixed-point iterations
    • K. Jbilou and H. Sadok, Some results about vector extrapolation methods and related fixed-point iterations, J. Comput. Appl. Math. 36 (1991) 385-398.
    • (1991) J. Comput. Appl. Math. , vol.36 , pp. 385-398
    • Jbilou, K.1    Sadok, H.2
  • 69
    • 0015141223 scopus 로고
    • Survey of extrapolation processes in numerical analysis
    • D.C. Joyce, Survey of extrapolation processes in numerical analysis, SIAM Rev. 13 (1971) 435-490.
    • (1971) SIAM Rev. , vol.13 , pp. 435-490
    • Joyce, D.C.1
  • 71
    • 0040832267 scopus 로고
    • Sur l'usage des fractions continues dans le calcul intégral
    • J.L. Lagrange, Sur l'usage des fractions continues dans le calcul intégral, Nouveaux Mém. Acad. Sci. Berlin 7 (1776) 236-264; Oeuvres 4 (1869) 301-322.
    • (1776) Nouveaux Mém. Acad. Sci. Berlin , vol.7 , pp. 236-264
    • Lagrange, J.L.1
  • 72
    • 0040237704 scopus 로고
    • J.L. Lagrange, Sur l'usage des fractions continues dans le calcul intégral, Nouveaux Mém. Acad. Sci. Berlin 7 (1776) 236-264; Oeuvres 4 (1869) 301-322.
    • (1869) Oeuvres , vol.4 , pp. 301-322
  • 73
    • 0000076718 scopus 로고
    • Observationes variae in mathesin puram
    • J.H. Lambert, Observationes variae in mathesin puram, Acta Helvetica 3 (1758) 128-168.
    • (1758) Acta Helvetica , vol.3 , pp. 128-168
    • Lambert, J.H.1
  • 74
    • 0001323667 scopus 로고
    • Un théorème de convergence pour le procédé d'extrapolation de richardson
    • P.J. Laurent, Un théorème de convergence pour le procédé d'extrapolation de Richardson, C. R. Acad. Sci. Paris 256 (1963) 1435-1437.
    • (1963) C. R. Acad. Sci. Paris , vol.256 , pp. 1435-1437
    • Laurent, P.J.1
  • 75
    • 0028480852 scopus 로고
    • On the stochastic acceleration of sequences of random variables
    • H. Lavastre, On the stochastic acceleration of sequences of random variables, Appl. Numer. Math. 15 (1994) 77-98.
    • (1994) Appl. Numer. Math. , vol.15 , pp. 77-98
    • Lavastre, H.1
  • 76
    • 0000168478 scopus 로고
    • Convergence of the topological ε-algorithm for solving systems of nonlinear equations
    • H. Le Ferrand, Convergence of the topological ε-algorithm for solving systems of nonlinear equations, Numerical Algor. 3 (1992) 273-284.
    • (1992) Numerical Algor. , vol.3 , pp. 273-284
    • Ferrand, H.L.1
  • 77
    • 84948301871 scopus 로고
    • Development of nonlinear transformations for improving convergence of sequences
    • D. Levin, Development of nonlinear transformations for improving convergence of sequences, Int. J. Comput. Math. B3 (1973) 371-388.
    • (1973) Int. J. Comput. Math. B , vol.3 , pp. 371-388
    • Levin, D.1
  • 78
    • 0039679035 scopus 로고
    • Ueber die zahl π
    • F. Lindemann, Ueber die Zahl π, Math. Ann. 20 (1882) 213-225.
    • (1882) Math. Ann. , vol.20 , pp. 213-225
    • Lindemann, F.1
  • 82
    • 0001679226 scopus 로고
    • A method of summing infinite series
    • S. Lubkin, A method of summing infinite series, J. Res. Nat. Bur. Stand. 48 (1952) 228-254.
    • (1952) J. Res. Nat. Bur. Stand. , vol.48 , pp. 228-254
    • Lubkin, S.1
  • 85
    • 0005338721 scopus 로고
    • Acceleration methods based on convergence tests
    • A.C. Matos, Acceleration methods based on convergence tests, Numer. Math. 58 (1990) 329-340.
    • (1990) Numer. Math. , vol.58 , pp. 329-340
    • Matos, A.C.1
  • 87
    • 0005355744 scopus 로고
    • Acceleration property for the columns of the E-algorithm
    • A.C. Matos and M. Prévost, Acceleration property for the columns of the E-algorithm, Numerical Algor. 2 (1992) 393-408.
    • (1992) Numerical Algor. , vol.2 , pp. 393-408
    • Matos, A.C.1    Prévost, M.2
  • 89
    • 0000321573 scopus 로고
    • A note on the ε-algorithm
    • J.B. McLeod, A note on the ε-algorithm, Computing 7 (1971) 17-24.
    • (1971) Computing , vol.7 , pp. 17-24
    • McLeod, J.B.1
  • 90
    • 0005318096 scopus 로고
    • Lower estimates for the error of the best uniform approximation
    • G. Meinardus and G.D. Taylor, Lower estimates for the error of the best uniform approximation, J. Approx. Theory 16 (1976) 150-161.
    • (1976) J. Approx. Theory , vol.16 , pp. 150-161
    • Meinardus, G.1    Taylor, G.D.2
  • 91
    • 0005279813 scopus 로고
    • Extension of Huygens' approximation to a circular arc
    • R.M. Milne, Extension of Huygens' approximation to a circular arc, Math. Gaz. 2 (1903) 309-311.
    • (1903) Math. Gaz. , vol.2 , pp. 309-311
    • Milne, R.M.1
  • 93
    • 85029991552 scopus 로고
    • Physique théorique: Les approximants de padé retrouvés
    • IREM de Lille, Lille
    • P. Moussa, Physique théorique: les approximants de Padé retrouvés, in: Approximants de Padé (IREM de Lille, Lille, 1994).
    • (1994) Approximants de Padé
    • Moussa, P.1
  • 94
    • 0002789316 scopus 로고
    • Neville-Aitken algorithms for interpolating by functions of Čebyšev-systems in the sense of Newton and in a generalized sense of Hermite
    • A.G. Law and B.N. Sahney, eds., Academic Press, New York
    • G. Mühlbach, Neville-Aitken algorithms for interpolating by functions of Čebyšev-systems in the sense of Newton and in a generalized sense of Hermite, in: A.G. Law and B.N. Sahney, eds., Theory of Approximation with Applications (Academic Press, New York, 1976) 200-212.
    • (1976) Theory of Approximation with Applications , pp. 200-212
    • Mühlbach, G.1
  • 95
    • 0005366827 scopus 로고
    • Studien zu fürstenau's neuer methode der darstellung und berechnung der wurzeln algebraischer gleichungen durch determinanten der coefficienten
    • H. Naegelsbach, Studien zu Fürstenau's neuer Methode der Darstellung und Berechnung der Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten, Arch. Math. Phys. 59 (1876) 147-192; 61 (1877) 19-85.
    • (1876) Arch. Math. Phys. , vol.59 , pp. 147-192
    • Naegelsbach, H.1
  • 96
    • 0039645917 scopus 로고
    • H. Naegelsbach, Studien zu Fürstenau's neuer Methode der Darstellung und Berechnung der Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten, Arch. Math. Phys. 59 (1876) 147-192; 61 (1877) 19-85.
    • (1877) Arch. Math. Phys. , vol.61 , pp. 19-85
  • 100
    • 0000544833 scopus 로고
    • Extended Aitken acceleration
    • K.J. Overholt, Extended Aitken acceleration, BIT 5 (1965) 122-132.
    • (1965) BIT , vol.5 , pp. 122-132
    • Overholt, K.J.1
  • 101
    • 0002664537 scopus 로고
    • Sur la représentation approchée d'une fonction par des fractions rationnelles
    • H. Padé, Sur la représentation approchée d'une fonction par des fractions rationnelles, Ann. Sci. Ec. Norm. Sup. 9 (1892) 1-93; also in: C. Brezinski, ed., Oeuvres (Librairie Scientifique et Technique Albert Blanchard, Paris, 1984) 72-166.
    • (1892) Ann. Sci. Ec. Norm. Sup. , vol.9 , pp. 1-93
    • Padé, H.1
  • 102
    • 0039645919 scopus 로고
    • Librairie Scientifique et Technique Albert Blanchard, Paris
    • H. Padé, Sur la représentation approchée d'une fonction par des fractions rationnelles, Ann. Sci. Ec. Norm. Sup. 9 (1892) 1-93; also in: C. Brezinski, ed., Oeuvres (Librairie Scientifique et Technique Albert Blanchard, Paris, 1984) 72-166.
    • (1984) Oeuvres , pp. 72-166
    • Brezinski, C.1
  • 103
    • 51249187889 scopus 로고
    • Le trasformazioni razionali di una successione
    • R. Pennacchi, Le trasformazioni razionali di una successione, Calcolo 5 (1968) 37-50.
    • (1968) Calcolo , vol.5 , pp. 37-50
    • Pennacchi, R.1
  • 105
    • 51249169077 scopus 로고
    • Acceleration property for the E-algorithm and an application to the summation of series
    • M. Prévost, Acceleration property for the E-algorithm and an application to the summation of series, Adv. Comput. Math. 2 (1994) 319-341.
    • (1994) Adv. Comput. Math. , vol.2 , pp. 319-341
    • Prévost, M.1
  • 107
    • 0000170864 scopus 로고
    • The approximate arithmetical solution by finite difference of physical problems involving differential equations, with an application to the stress in a masonry dam
    • L.F. Richardson, The approximate arithmetical solution by finite difference of physical problems involving differential equations, with an application to the stress in a masonry dam, Philos. Trans. Roy. Soc. London Ser. A 210 (1910) 307-357.
    • (1910) Philos. Trans. Roy. Soc. London Ser. A , vol.210 , pp. 307-357
    • Richardson, L.F.1
  • 108
    • 0000202520 scopus 로고
    • The deferred approach to the limit, I: Single lattice
    • L.F. Richardson, The deferred approach to the limit, I: Single lattice, Philos. Trans. Roy. Soc. London Ser. A 226 (1927) 299-349.
    • (1927) Philos. Trans. Roy. Soc. London Ser. A , vol.226 , pp. 299-349
    • Richardson, L.F.1
  • 109
    • 0002434398 scopus 로고
    • Vereinfachte numerische Integration
    • W. Romberg, Vereinfachte numerische Integration, Kgl. Norske Vid. Selsk. Forsk. 28 (1955) 30-36.
    • (1955) Kgl. Norske Vid. Selsk. Forsk. , vol.28 , pp. 30-36
    • Romberg, W.1
  • 110
    • 0010843126 scopus 로고
    • Der quotienten-differenzen-algorithmus
    • H. Rutishauser, Der Quotienten-Differenzen-Algorithmus, Z. Angew. Math. Phys. 5 (1954) 233-251.
    • (1954) Z. Angew. Math. Phys. , vol.5 , pp. 233-251
    • Rutishauser, H.1
  • 111
    • 0040237695 scopus 로고
    • Bestimmung der eigenwerte und eigenvektoren einer matrix mit hilfe des quotienten-differenzen-algorithmus
    • H. Rutishauser, Bestimmung der Eigenwerte und Eigenvektoren einer Matrix mit Hilfe des Quotienten-Differenzen-Algorithmus, Z. Angew. Math. Phys. 6 (1955) 387-401.
    • (1955) Z. Angew. Math. Phys. , vol.6 , pp. 387-401
    • Rutishauser, H.1
  • 112
    • 0002712872 scopus 로고
    • Ausdehnung des rombergschen prinzips
    • H. Rutishauser, Ausdehnung des Rombergschen Prinzips, Numer. Math. 5 (1963) 48-54.
    • (1963) Numer. Math. , vol.5 , pp. 48-54
    • Rutishauser, H.1
  • 113
    • 21144483373 scopus 로고
    • Quasilinear vector extrapolation methods
    • H. Sadok, Quasilinear vector extrapolation methods, Linear Alg. Appl. 190 (1993) 71-85.
    • (1993) Linear Alg. Appl. , vol.190 , pp. 71-85
    • Sadok, H.1
  • 115
    • 0005389516 scopus 로고
    • Non-commutative extrapolation algorithms
    • A. Salam, Non-commutative extrapolation algorithms, Numerical Algor. 7 (1994) 225-251.
    • (1994) Numerical Algor. , vol.7 , pp. 225-251
    • Salam, A.1
  • 116
    • 0005425422 scopus 로고
    • On the numerical solution of linear simultaneous equations by an iterative method
    • J.R. Schmidt, On the numerical solution of linear simultaneous equations by an iterative method, Phil. Mag. 7 (1941) 369-383.
    • (1941) Phil. Mag. , vol.7 , pp. 369-383
    • Schmidt, J.R.1
  • 117
    • 0000064704 scopus 로고
    • Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen
    • C. Schneider, Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialfällen, Numer. Math. 24 (1975) 177-184.
    • (1975) Numer. Math. , vol.24 , pp. 177-184
    • Schneider, C.1
  • 119
    • 85171863190 scopus 로고
    • Non linear transformations of divergent and slowly convergent sequences
    • D. Shanks, Non linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955) 1-42.
    • (1955) J. Math. Phys. , vol.34 , pp. 1-42
    • Shanks, D.1
  • 120
  • 121
    • 0023995271 scopus 로고
    • Extrapolation vs. Projection methods for linear systems of equations
    • A. Sidi, Extrapolation vs. projection methods for linear systems of equations, J. Comput. Appl. Math. 22 (1988) 71-88.
    • (1988) J. Comput. Appl. Math. , vol.22 , pp. 71-88
    • Sidi, A.1
  • 122
    • 0001735812 scopus 로고
    • On a generalization of the Richardson extrapolation process
    • A. Sidi, On a generalization of the Richardson extrapolation process, Numer. Math. 57 (1990) 365-377.
    • (1990) Numer. Math. , vol.57 , pp. 365-377
    • Sidi, A.1
  • 124
    • 84982371828 scopus 로고
    • Altes und neues über numerische quadratur
    • E. Stiefel, Altes und neues über numerische Quadratur, Z. Angew. Math. Mech. 41 (1961) 408-413.
    • (1961) Z. Angew. Math. Mech. , vol.41 , pp. 408-413
    • Stiefel, E.1
  • 125
    • 0042435452 scopus 로고
    • Sur la réduction en fraction continue d'une série procédant suivant les puissances descendantes d'une variable
    • T.J. Stieltjes, Sur la réduction en fraction continue d'une série procédant suivant les puissances descendantes d'une variable, Ann. Fac. Sci. Toulouse 3 (1889) H. 1-17.
    • (1889) Ann. Fac. Sci. Toulouse , vol.3
    • Stieltjes, T.J.1
  • 126
    • 0002593008 scopus 로고
    • Recherches sur les fractions continues
    • T.J. Stieltjes, Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse 8 (1894) 1-122.
    • (1894) Ann. Fac. Sci. Toulouse , vol.8 , pp. 1-122
    • Stieltjes, T.J.1
  • 128
    • 0039645920 scopus 로고
    • Vector Padé approximants
    • R. Vichnevetsky and J. Vignes, eds., North-Holland, Amsterdam
    • J. van Iseghem, Vector Padé approximants, in: R. Vichnevetsky and J. Vignes, eds., Numerical Mathematics and Applications (North-Holland, Amsterdam, 1985) 73-77.
    • (1985) Numerical Mathematics and Applications , pp. 73-77
    • Van Iseghem, J.1
  • 129
    • 0023378740 scopus 로고
    • Vector orthogonal relations. Vector QD algorithm
    • J. van Iseghem, Vector orthogonal relations. Vector QD algorithm, J. Comput. Appl. Math. 19 (1987) 141-150.
    • (1987) J. Comput. Appl. Math. , vol.19 , pp. 141-150
    • Van Iseghem, J.1
  • 130
    • 21844525774 scopus 로고
    • Convergence of vectorial sequences. Applications
    • J. van Iseghem, Convergence of vectorial sequences. Applications, Numer. Math. 68 (1994) 549-562.
    • (1994) Numer. Math. , vol.68 , pp. 549-562
    • Van Iseghem, J.1
  • 133
    • 0343863901 scopus 로고
    • Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series
    • E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Physics Reports 10 (1989) 189-371.
    • (1989) Comput. Physics Reports , vol.10 , pp. 189-371
    • Weniger, E.J.1
  • 135
    • 84968519483 scopus 로고
    • n) transformation
    • n) transformation, MTAC 10 (1956) 91-96.
    • (1956) MTAC , vol.10 , pp. 91-96
    • Wynn, P.1
  • 136
    • 84971178657 scopus 로고
    • On a procrustean technique for the numerical transformation of slowly convergent sequences and series
    • P. Wynn, On a procrustean technique for the numerical transformation of slowly convergent sequences and series, Proc. Cambridge Phil. Soc. 52 (1956) 663-671.
    • (1956) Proc. Cambridge Phil. Soc. , vol.52 , pp. 663-671
    • Wynn, P.1
  • 137
    • 84968509237 scopus 로고
    • Acceleration techniques for iterated vector and matrix problems
    • P. Wynn, Acceleration techniques for iterated vector and matrix problems, Math. Comp. 16 (1962) 301-322.
    • (1962) Math. Comp. , vol.16 , pp. 301-322
    • Wynn, P.1
  • 138
    • 0001331675 scopus 로고
    • Singular rules for certain nonlinear algorithms
    • P. Wynn, Singular rules for certain nonlinear algorithms, BIT 3 (1963) 175-195.
    • (1963) BIT , vol.3 , pp. 175-195
    • Wynn, P.1


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