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Volumn 122, Issue 1, 2000, Pages 329-356

Prediction properties of Aitken's iterated Δ2 process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; RECURSIVE FUNCTIONS;

EID: 0034289876     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00363-0     Document Type: Article
Times cited : (28)

References (119)
  • 1
    • 0000665315 scopus 로고
    • On Bernoulli's numerical solution of algebraic equations
    • A.C. Aitken, On Bernoulli's numerical solution of algebraic equations, Proc. Roy. Soc. Edinburgh 46 (1926) 289-305.
    • (1926) Proc. Roy. Soc. Edinburgh , vol.46 , pp. 289-305
    • Aitken, A.C.1
  • 3
    • 0002234355 scopus 로고
    • The theory and application of the Padé approximant method
    • G.A. Baker Jr., The theory and application of the Padé approximant method, Adv. Theoret. Phys. 1 (1965) 1-58.
    • (1965) Adv. Theoret. Phys. , vol.1 , pp. 1-58
    • Baker G.A., Jr.1
  • 6
    • 84927198753 scopus 로고
    • The Padé approximant and related material
    • D. Bessis (Ed.), Gordon and Breach, New York
    • G.A. Baker Jr., The Padé approximant and related material, in: D. Bessis (Ed.), Cargèse Lectures in Physics, Vol. 5, Gordon and Breach, New York, 1972, pp. 349-383.
    • (1972) Cargèse Lectures in Physics , vol.5 , pp. 349-383
    • Baker G.A., Jr.1
  • 9
    • 84987012289 scopus 로고
    • The Padé approximation and its physical applications
    • J.L. Basdevant, The Padé approximation and its physical applications, Fortschr. Phys. 20 (1972) 283-331.
    • (1972) Fortschr. Phys. , vol.20 , pp. 283-331
    • Basdevant, J.L.1
  • 10
    • 0021314783 scopus 로고
    • Aitken acceleration of some alternating series
    • G.E. Bell, G.M. Phillips, Aitken acceleration of some alternating series, BIT 24 (1984) 70-77.
    • (1984) BIT , vol.24 , pp. 70-77
    • Bell, G.E.1    Phillips, G.M.2
  • 11
    • 0002614887 scopus 로고
    • Iterations of convergence accelerating nonlinear transforms
    • S. Bhowmick, R. Bhattacharya, D. Roy, Iterations of convergence accelerating nonlinear transforms, Comput. Phys. Comm. 54 (1989) 31-36.
    • (1989) Comput. Phys. Comm. , vol.54 , pp. 31-36
    • Bhowmick, S.1    Bhattacharya, R.2    Roy, D.3
  • 13
    • 0000701158 scopus 로고
    • Accélération de suites à convergence logarithmique
    • C. Brezinski, Accélération de suites à convergence logarithmique, C. R. Acad. Sci. Paris 273 (1971) 727-730.
    • (1971) C. R. Acad. Sci. Paris , vol.273 , pp. 727-730
    • Brezinski, C.1
  • 14
    • 0005477425 scopus 로고
    • A bibliography on Padé approximation and related matters
    • H. Cabannes (Ed.), Springer, Berlin
    • C. Brezinski, A bibliography on Padé approximation and related matters, in: H. Cabannes (Ed.), Padé Approximation Method and Its Application to Mechanics, Springer, Berlin, 1976, pp. 245-267.
    • (1976) Padé Approximation Method and Its Application to Mechanics , pp. 245-267
    • Brezinski, C.1
  • 18
    • 0000202795 scopus 로고
    • Prediction properties of some extrapolation methods
    • C. Brezinski, Prediction properties of some extrapolation methods, Appl. Numer. Math. 1 (1985) 457-462.
    • (1985) Appl. Numer. Math. , vol.1 , pp. 457-462
    • Brezinski, C.1
  • 22
    • 0030103537 scopus 로고    scopus 로고
    • Extrapolation algorithms and Padé approximations: A historical survey
    • C. Brezinski, Extrapolation algorithms and Padé approximations: a historical survey, Appl. Numer. Math. 20 (1996) 299-318.
    • (1996) Appl. Numer. Math. , vol.20 , pp. 299-318
    • Brezinski, C.1
  • 24
    • 70350315109 scopus 로고
    • Padé approximations
    • P.G. Ciarlet, J.L. Lions (Eds.), North-Holland, Amsterdam
    • C. Brezinski, J. Van Iseghem, Padé approximations, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis III, North-Holland, Amsterdam, 1994, pp. 47-222.
    • (1994) Handbook of Numerical Analysis III , pp. 47-222
    • Brezinski, C.1    Van Iseghem, J.2
  • 25
    • 0002973253 scopus 로고
    • A taste of Padé approximation
    • A. Iserles (Ed.), Cambridge University Press, Cambridge
    • C. Brezinski, J. Van Iseghem, A taste of Padé approximation, in: A. Iserles (Ed.), Acta Numerica 1995, Cambridge University Press, Cambridge, 1995, pp. 53-103.
    • (1995) Acta Numerica 1995 , pp. 53-103
    • Brezinski, C.1    Van Iseghem, J.2
  • 27
    • 0000070726 scopus 로고    scopus 로고
    • Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams
    • S.J. Brodsky, J. Ellis, E. Gardi, M. Karliner, M.A. Samuel, Padé approximants, optimal renormalization scales, and momentum flow in Feynman diagrams, Phys. Rev. D 56 (1998) 6980-6992.
    • (1998) Phys. Rev. D , vol.56 , pp. 6980-6992
    • Brodsky, S.J.1    Ellis, J.2    Gardi, E.3    Karliner, M.4    Samuel, M.A.5
  • 31
    • 0005392363 scopus 로고    scopus 로고
    • Asymptotic Padé-approximant method and QCD current correlation functions
    • F. Chishstie, V. Elias, T.G. Steele, Asymptotic Padé-approximant method and QCD current correlation functions, Phys. Rev. D 59 (1999) 10513-1-10513-10.
    • (1999) Phys. Rev. D , vol.59 , pp. 105131-1051310
    • Chishstie, F.1    Elias, V.2    Steele, T.G.3
  • 32
    • 0000983349 scopus 로고
    • Bulk properties from finite cluster calculations. VIII. Benchmark calculations on the efficiency of extrapolation methods for the HF and MP2 energies of polyacenes
    • J. Cioslowski, E.J. Weniger, Bulk properties from finite cluster calculations. VIII. Benchmark calculations on the efficiency of extrapolation methods for the HF and MP2 energies of polyacenes, J. Comput. Chem. 14 (1993) 1468-1481.
    • (1993) J. Comput. Chem. , vol.14 , pp. 1468-1481
    • Cioslowski, J.1    Weniger, E.J.2
  • 33
    • 84987133662 scopus 로고
    • Examples on the use of symbolic computation in physics and chemistry: Applications of the inner projection technique and of a new summation method for divergent series
    • J. Čížek, F. Vinette, E.J. Weniger, Examples on the use of symbolic computation in physics and chemistry: applications of the inner projection technique and of a new summation method for divergent series, Internat. J. Quantum Chem. Symp. 25 (1991) 209-223.
    • (1991) Internat. J. Quantum Chem. Symp. , vol.25 , pp. 209-223
    • Čížek, J.1    Vinette, F.2    Weniger, E.J.3
  • 35
    • 84865917980 scopus 로고
    • Large order perturbation theory in the context of atomic and molecular physics - interdisciplinary aspects
    • J. Čížek, E.R. Vrscay, Large order perturbation theory in the context of atomic and molecular physics - interdisciplinary aspects, Internat. J. Quantum Chem. 21 (1982) 27-68.
    • (1982) Internat. J. Quantum Chem. , vol.21 , pp. 27-68
    • Čížek, J.1    Vrscay, E.R.2
  • 36
    • 0000905803 scopus 로고    scopus 로고
    • Effective characteristic polynomials and two-point Padé approximants as summation techniques for the strongly divergent perturbation expansions of the ground state energies of anharmonic oscillators
    • J. Čížek, E.J. Weniger, P. Bracken, V. Spirko, Effective characteristic polynomials and two-point Padé approximants as summation techniques for the strongly divergent perturbation expansions of the ground state energies of anharmonic oscillators, Phys. Rev. E 53 (1996) 2925-2939.
    • (1996) Phys. Rev. E , vol.53 , pp. 2925-2939
    • Čížek, J.1    Weniger, E.J.2    Bracken, P.3    Spirko, V.4
  • 45
    • 0000961645 scopus 로고
    • Summing a common type of slowly convergent series of positive terms
    • J.E. Drummond, Summing a common type of slowly convergent series of positive terms, J. Austral. Math. Soc. B 19 (1976) 416-421.
    • (1976) J. Austral. Math. Soc. B , vol.19 , pp. 416-421
    • Drummond, J.E.1
  • 46
    • 0542373759 scopus 로고    scopus 로고
    • Padé improvement of QCD running coupling constants, running masses, Higgs decay rates, and scalar channel sum rules
    • V. Elias, T.G. Steele, F. Chishtie, R. Migneron, K. Sprague, Padé improvement of QCD running coupling constants, running masses, Higgs decay rates, and scalar channel sum rules, Phys. Rev. D 58 (1998) 116007.
    • (1998) Phys. Rev. D , vol.58 , pp. 116007
    • Elias, V.1    Steele, T.G.2    Chishtie, F.3    Migneron, R.4    Sprague, K.5
  • 47
    • 0002755633 scopus 로고    scopus 로고
    • Padé approximants, Borel transforms and renormalons: The Bjorken sum rule as a case study
    • J. Ellis, E. Gardi, M. Karliner, M.A. Samuel, Padé approximants, Borel transforms and renormalons: the Bjorken sum rule as a case study, Phys. Lett. B 366 (1996) 268-275.
    • (1996) Phys. Lett. B , vol.366 , pp. 268-275
    • Ellis, J.1    Gardi, E.2    Karliner, M.3    Samuel, M.A.4
  • 48
    • 0000222955 scopus 로고    scopus 로고
    • Renormalization-scheme dependence of Padé summation in QCD
    • J. Ellis, E. Gardi, M. Karliner, M.A. Samuel, Renormalization-scheme dependence of Padé summation in QCD, Phys. Rev. D 54 (1996) 6986-6996.
    • (1996) Phys. Rev. D , vol.54 , pp. 6986-6996
    • Ellis, J.1    Gardi, E.2    Karliner, M.3    Samuel, M.A.4
  • 49
    • 0000556099 scopus 로고    scopus 로고
    • Asymptotic Padé approximant predictions: Up to five loops in QCD and SQCD
    • J. Ellis, I. Jack, D.R.T. Jones, M. Karliner, M.A. Samuel, Asymptotic Padé approximant predictions: up to five loops in QCD and SQCD, Phys. Rev. D 57 (1998) 2665-2675.
    • (1998) Phys. Rev. D , vol.57 , pp. 2665-2675
    • Ellis, J.1    Jack, I.2    Jones, D.R.T.3    Karliner, M.4    Samuel, M.A.5
  • 50
    • 0039386413 scopus 로고    scopus 로고
    • A prediction for the 4-loop β function in QCD
    • J. Ellis, M. Karliner, M.A. Samuel, A prediction for the 4-loop β function in QCD, Phys. Lett. B 400 (1997) 176-181.
    • (1997) Phys. Lett. B , vol.400 , pp. 176-181
    • Ellis, J.1    Karliner, M.2    Samuel, M.A.3
  • 51
    • 0001998544 scopus 로고
    • Numerical detection of the best Padé approximant and determination of the Fourier coefficients of the insufficiently sampled functions
    • P.R. Graves-Morris (Ed.), Academic Press, London
    • J. Gilewicz, Numerical detection of the best Padé approximant and determination of the Fourier coefficients of the insufficiently sampled functions, in: P.R. Graves-Morris (Ed.), Padé Approximants and their Applications, Academic Press, London, 1973, pp. 99-103.
    • (1973) Padé Approximants and Their Applications , pp. 99-103
    • Gilewicz, J.1
  • 54
    • 36749106008 scopus 로고
    • Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators
    • S. Graffi, V. Grecchi, Borel summability and indeterminacy of the Stieltjes moment problem: application to the anharmonic oscillators, J. Math. Phys. 19 (1978) 1002-1006.
    • (1978) J. Math. Phys. , vol.19 , pp. 1002-1006
    • Graffi, S.1    Grecchi, V.2
  • 55
    • 0015283390 scopus 로고
    • The Padé table and its relation to certain algorithms of numerical analysis
    • W.B. Gragg, The Padé table and its relation to certain algorithms of numerical analysis, SIAM Rev. 14 (1972) 1-62.
    • (1972) SIAM Rev. , vol.14 , pp. 1-62
    • Gragg, W.B.1
  • 59
    • 4244009832 scopus 로고
    • Efficient evaluation of infinite-series representations for overlap, two-center nuclear attraction, and Coulomb integrals using nonlinear convergence accelerators
    • J. Grotendorst, E.J. Weniger, E.O. Steinborn, Efficient evaluation of infinite-series representations for overlap, two-center nuclear attraction, and Coulomb integrals using nonlinear convergence accelerators, Phys. Rev. A 33 (1986) 3706-3726.
    • (1986) Phys. Rev. A , vol.33 , pp. 3706-3726
    • Grotendorst, J.1    Weniger, E.J.2    Steinborn, E.O.3
  • 60
    • 0001380252 scopus 로고
    • Méthode d'Aitken itérée pour les suites oscillantes d'approximations
    • P. Hillion, Méthode d'Aitken itérée pour les suites oscillantes d'approximations, C. R. Acad. Sci. Paris A 280 (1975) 1701-1704.
    • (1975) C. R. Acad. Sci. Paris A , vol.280 , pp. 1701-1704
    • Hillion, P.1
  • 61
    • 0029408759 scopus 로고
    • On remainder estimates for Levin-type sequence transformations
    • H.H.H. Homeier, E.J. Weniger, On remainder estimates for Levin-type sequence transformations, Comput. Phys. Comm. 92 (1995) 1-10.
    • (1995) Comput. Phys. Comm. , vol.92 , pp. 1-10
    • Homeier, H.H.H.1    Weniger, E.J.2
  • 63
    • 0032760685 scopus 로고    scopus 로고
    • Convergence acceleration via combined nonlinear-condensation transformations
    • U.D. Jentschura, P.J. Mohr, G. Soff, E.J. Weniger, Convergence acceleration via combined nonlinear-condensation transformations, Comput. Phys. Comm. 116 (1999) 28-54.
    • (1999) Comput. Phys. Comm. , vol.116 , pp. 28-54
    • Jentschura, U.D.1    Mohr, P.J.2    Soff, G.3    Weniger, E.J.4
  • 65
    • 0005472382 scopus 로고    scopus 로고
    • Precise estimates of high orders in QCD
    • M. Karliner, Precise estimates of high orders in QCD, Acta Phys. Polon. B 29 (1998) 1505-1520.
    • (1998) Acta Phys. Polon. B , vol.29 , pp. 1505-1520
    • Karliner, M.1
  • 66
    • 0000746091 scopus 로고
    • Eine neue Methode, die numerischen Summen langsam convergirender Reihen zu berechnen
    • E.E. Kummer, Eine neue Methode, die numerischen Summen langsam convergirender Reihen zu berechnen, J. Reine Angew. Math. 16 (1837) 206-214.
    • (1837) J. Reine Angew. Math. , vol.16 , pp. 206-214
    • Kummer, E.E.1
  • 68
    • 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
  • 71
    • 84966247330 scopus 로고
    • Aitken sequences and generalized Fibonacci numbers
    • J.H. McCabe, G.M. Phillips, Aitken sequences and generalized Fibonacci numbers, Math. Comp. 45 (1985) 553-558.
    • (1985) Math. Comp. , vol.45 , pp. 553-558
    • McCabe, J.H.1    Phillips, G.M.2
  • 74
    • 0023378728 scopus 로고
    • Convergence acceleration of logarithmic fixed point sequences
    • P. Sablonniere, Convergence acceleration of logarithmic fixed point sequences, J. Comput. Appl. Math. 19 (1987) 55-60.
    • (1987) J. Comput. Appl. Math. , vol.19 , pp. 55-60
    • Sablonniere, P.1
  • 75
    • 0005442781 scopus 로고
    • Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences
    • P. Sablonniere, Comparison of four algorithms accelerating the convergence of a subset of logarithmic fixed point sequences, Numer. Algorithms 1 (1991) 177-197.
    • (1991) Numer. Algorithms , vol.1 , pp. 177-197
    • Sablonniere, P.1
  • 76
    • 0000418587 scopus 로고
    • 2 transforms on some slowly convergent sequences
    • 2 transforms on some slowly convergent sequences, Numer. Algorithms 3 (1992) 401-409.
    • (1992) Numer. Algorithms , vol.3 , pp. 401-409
    • Sablonniere, P.1
  • 77
    • 0005426032 scopus 로고
    • Comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences
    • P. Sablonniere, Comparison of four nonlinear transforms on some classes of logarithmic fixed point sequences, J. Comput. Appl. Math. 62 (1995) 103-128.
    • (1995) J. Comput. Appl. Math. , vol.62 , pp. 103-128
    • Sablonniere, P.1
  • 79
    • 0039243985 scopus 로고    scopus 로고
    • s, from W + jet processes: An analysis using Padé approximants
    • s, from W + jet processes: an analysis using Padé approximants, Phys. Lett. B 394 (1997) 165-169.
    • (1997) Phys. Lett. B , vol.394 , pp. 165-169
    • Samuel, M.A.1    Abraha, T.2    Yu, J.3
  • 80
    • 0000723321 scopus 로고
    • Comparison of the Padé approximation method to perturbative QCD calculations
    • M.A. Samuel, J. Ellis, M. Karliner, Comparison of the Padé approximation method to perturbative QCD calculations, Phys. Rev. Lett. 74 (1995) 4380-4383.
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 4380-4383
    • Samuel, M.A.1    Ellis, J.2    Karliner, M.3
  • 81
    • 0642358297 scopus 로고
    • Estimating perturbative coefficients in quantum field theory and the ortho-positronium decay rate discrepancy
    • M.A. Samuel, G. Li, Estimating perturbative coefficients in quantum field theory and the ortho-positronium decay rate discrepancy, Phys. Lett. B 331 (1994) 114-118.
    • (1994) Phys. Lett. B , vol.331 , pp. 114-118
    • Samuel, M.A.1    Li, G.2
  • 82
    • 0000122837 scopus 로고
    • Estimating perturbative coefficients in quantum field theory using Padé approximants
    • M.A. Samuel, G. Li, E. Steinfelds, Estimating perturbative coefficients in quantum field theory using Padé approximants, Phys. Rev. D 48 (1993) 869-872.
    • (1993) Phys. Rev. D , vol.48 , pp. 869-872
    • Samuel, M.A.1    Li, G.2    Steinfelds, E.3
  • 83
    • 33750637703 scopus 로고
    • Estimating perturbative coefficients in quantum field theory and statistical physics
    • Erratum, Phys. Rev. E 55 (1997) 2072
    • M.A. Samuel, G. Li, E. Steinfelds, Estimating perturbative coefficients in quantum field theory and statistical physics, Phys. Rev. E 51 (1995) 3911-3933; Erratum, Phys. Rev. E 55 (1997) 2072.
    • (1995) Phys. Rev. E , vol.51 , pp. 3911-3933
    • Samuel, M.A.1    Li, G.2    Steinfelds, E.3
  • 84
    • 85171863190 scopus 로고
    • Non-linear transformations of divergent and slowly convergent sequences
    • Cambridge, MA
    • D. Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math, and Phys. (Cambridge, MA) 34 (1955) 1-42.
    • (1955) J. Math, and Phys. , vol.34 , pp. 1-42
    • Shanks, D.1
  • 85
    • 0000106169 scopus 로고
    • Prediction properties of the t-transformation
    • A. Sidi, D. Levin, Prediction properties of the t-transformation, SIAM J. Numer. Anal. 20 (1983) 589-598.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 589-598
    • Sidi, A.1    Levin, D.2
  • 86
    • 84984068436 scopus 로고
    • Large orders and summability of eigenvalue perturbation theory: A mathematical overview
    • B. Simon, Large orders and summability of eigenvalue perturbation theory: a mathematical overview, Internat. J. Quantum Chem. 21 (1982) 3-25.
    • (1982) Internat. J. Quantum Chem. , vol.21 , pp. 3-25
    • Simon, B.1
  • 87
    • 0003105647 scopus 로고
    • Acceleration of linear and logarithmic convergence
    • D.A. Smith, W.F. Ford, Acceleration of linear and logarithmic convergence, SIAM J. Numer. Anal. 16 (1979) 223-240.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 223-240
    • Smith, D.A.1    Ford, W.F.2
  • 88
    • 84968476219 scopus 로고
    • Numerical comparisons of nonlinear convergence accelerators
    • D.A. Smith, W.F. Ford, Numerical comparisons of nonlinear convergence accelerators, Math. Comp. 38 (1982) 481-499.
    • (1982) Math. Comp. , vol.38 , pp. 481-499
    • Smith, D.A.1    Ford, W.F.2
  • 90
    • 0002434540 scopus 로고
    • Sequence transformations for the efficient evaluation of infinite series representations of some molecular integrals with exponentially decaying basis functions
    • E.O. Steinborn, E.J. Weniger, Sequence transformations for the efficient evaluation of infinite series representations of some molecular integrals with exponentially decaying basis functions, J. Mol. Struct. (Theochem) 210 (1990) 71-78.
    • (1990) J. Mol. Struct. (Theochem) , vol.210 , pp. 71-78
    • Steinborn, E.O.1    Weniger, E.J.2
  • 91
    • 0002461407 scopus 로고
    • Motivation for working in numerical analysis
    • J. Todd (Ed.), McGraw-Hill, New York
    • J. Todd, Motivation for working in numerical analysis, in: J. Todd (Ed.), Survey of Numerical Analysis, McGraw-Hill, New York, 1962, pp. 1-26.
    • (1962) Survey of Numerical Analysis , pp. 1-26
    • Todd, J.1
  • 92
    • 84972496721 scopus 로고
    • 2 process and related topics
    • 2 process and related topics, Pacific J. Math. 22 (1967) 349-359.
    • (1967) Pacific J. Math. , vol.22 , pp. 349-359
    • Tucker, R.R.1
  • 93
    • 84972573027 scopus 로고
    • 2 process and related topics II
    • 2 process and related topics II, Pacific J. Math. 28 (1969) 455-463.
    • (1969) Pacific J. Math. , vol.28 , pp. 455-463
    • Tucker, R.R.1
  • 95
    • 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. Phys. Rep. 10 (1989) 189-371.
    • (1989) Comput. Phys. Rep. , vol.10 , pp. 189-371
    • Weniger, E.J.1
  • 96
    • 0001673044 scopus 로고
    • On the summation of some divergent hypergeometric series and related perturbation expansions
    • E.J. Weniger, On the summation of some divergent hypergeometric series and related perturbation expansions, J. Comput. Appl. Math. 32 (1990) 291-300.
    • (1990) J. Comput. Appl. Math. , vol.32 , pp. 291-300
    • Weniger, E.J.1
  • 97
    • 0026141256 scopus 로고
    • On the derivation of iterated sequence transformations for the acceleration of convergence and the summation of divergent series
    • E.J. Weniger, On the derivation of iterated sequence transformations for the acceleration of convergence and the summation of divergent series, Comput. Phys. Comm. 64 (1991) 19-45.
    • (1991) Comput. Phys. Comm. , vol.64 , pp. 19-45
    • Weniger, E.J.1
  • 98
    • 0001375733 scopus 로고
    • Interpolation between sequence transformations
    • E.J. Weniger, Interpolation between sequence transformations, Numer. Algorithms 3 (1992) 477-486.
    • (1992) Numer. Algorithms , vol.3 , pp. 477-486
    • Weniger, E.J.1
  • 99
    • 0005480572 scopus 로고
    • On the efficiency of linear but nonregular sequence transformations
    • A. Cuyt (Ed.), Kluwer, Dordrecht
    • E.J. Weniger, On the efficiency of linear but nonregular sequence transformations, in: A. Cuyt (Ed.), Nonlinear Numerical Methods and Rational Approximation II, Kluwer, Dordrecht, 1994, pp. 269-282.
    • (1994) Nonlinear Numerical Methods and Rational Approximation II , pp. 269-282
    • Weniger, E.J.1
  • 101
    • 0001407401 scopus 로고    scopus 로고
    • Nonlinear sequence transformations: A computational tool for quantum mechanical and quantum chemical calculations
    • Erratum, Internat. J. Quantum Chem. 58 (1996) 319-321
    • E.J. Weniger, Nonlinear sequence transformations: a computational tool for quantum mechanical and quantum chemical calculations, Internat. J. Quantum Chem. 57 (1996) 265-280; Erratum, Internat. J. Quantum Chem. 58 (1996) 319-321.
    • (1996) Internat. J. Quantum Chem. , vol.57 , pp. 265-280
    • Weniger, E.J.1
  • 102
    • 0030600707 scopus 로고    scopus 로고
    • A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator
    • E.J. Weniger, A convergent renormalized strong coupling perturbation expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator, Ann. Phys. (NY) 246 (1996) 133-165.
    • (1996) Ann. Phys. (NY) , vol.246 , pp. 133-165
    • Weniger, E.J.1
  • 103
    • 0030247552 scopus 로고    scopus 로고
    • Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations
    • E.J. Weniger, Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations, Comput. Phys. 10 (1996) 496-503.
    • (1996) Comput. Phys. , vol.10 , pp. 496-503
    • Weniger, E.J.1
  • 104
    • 4243381828 scopus 로고    scopus 로고
    • Construction of the strong coupling expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator via a renormalized strong coupling expansion
    • E.J. Weniger, Construction of the strong coupling expansion for the ground state energy of the quartic, sextic, and octic anharmonic oscillator via a renormalized strong coupling expansion, Phys. Rev. Lett. 77 (1996) 2859-2862.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 2859-2862
    • Weniger, E.J.1
  • 105
    • 0001649615 scopus 로고    scopus 로고
    • Performance of superconvergent perturbation theory
    • E.J. Weniger, Performance of superconvergent perturbation theory, Phys. Rev. A 56 (1997) 5165-5168.
    • (1997) Phys. Rev. A , vol.56 , pp. 5165-5168
    • Weniger, E.J.1
  • 106
    • 0025453396 scopus 로고
    • Rational approximations for the modified Bessel function of the second kind
    • E.J. Weniger, J. Čížek, Rational approximations for the modified Bessel function of the second kind, Comput. Phys. Comm. 59 (1990) 471-493.
    • (1990) Comput. Phys. Comm. , vol.59 , pp. 471-493
    • Weniger, E.J.1    Čížek, J.2
  • 107
    • 0000254445 scopus 로고
    • Very accurate summation for the infinite coupling limit of the perturbation series expansions of anharmonic oscillators
    • E.J. Weniger, J. Čížek, F. Vinette, Very accurate summation for the infinite coupling limit of the perturbation series expansions of anharmonic oscillators, Phys. Lett. A 156 (1991) 169-174.
    • (1991) Phys. Lett. A , vol.156 , pp. 169-174
    • Weniger, E.J.1    Čížek, J.2    Vinette, F.3
  • 108
    • 34848924872 scopus 로고
    • The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations
    • E.J. Weniger, J. Čížek, F. Vinette, The summation of the ordinary and renormalized perturbation series for the ground state energy of the quartic, sextic, and octic anharmonic oscillators using nonlinear sequence transformations, J. Math. Phys. 34 (1993) 571-609.
    • (1993) J. Math. Phys. , vol.34 , pp. 571-609
    • Weniger, E.J.1    Čížek, J.2    Vinette, F.3
  • 110
    • 84986493479 scopus 로고
    • Extrapolation of finite cluster and crystal-orbital calculations on trans-polyacetylene
    • E.J. Weniger, C.-M. Liegener, Extrapolation of finite cluster and crystal-orbital calculations on trans-polyacetylene, Internat. J. Quantum Chem. 38 (1990) 55-74.
    • (1990) Internat. J. Quantum Chem. , vol.38 , pp. 55-74
    • Weniger, E.J.1    Liegener, C.-M.2
  • 111
    • 0002305925 scopus 로고
    • Nonlinear sequence transformations for the efficient evaluation of auxiliary functions for GTO molecular integrals
    • M. Defranceschi, J. Delhalle (Eds.), Kluwer, Dordrecht
    • E.J. Weniger, E.O. Steinborn, Nonlinear sequence transformations for the efficient evaluation of auxiliary functions for GTO molecular integrals, in: M. Defranceschi, J. Delhalle (Eds.), Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules, Kluwer, Dordrecht, 1989, pp. 341-346.
    • (1989) Numerical Determination of the Electronic Structure of Atoms, Diatomic and Polyatomic Molecules , pp. 341-346
    • Weniger, E.J.1    Steinborn, E.O.2
  • 115
    • 0005391359 scopus 로고
    • Commented bibliography on techniques for computing Padé approximants
    • L. Wuytack (Ed.), Springer, Berlin
    • L. Wuytack, Commented bibliography on techniques for computing Padé approximants, in: L. Wuytack (Ed.), Padé Approximation and its Applications, Springer, Berlin, 1979, pp. 375-392.
    • (1979) Padé Approximation and Its Applications , pp. 375-392
    • Wuytack, L.1
  • 117
    • 0002794989 scopus 로고
    • On the convergence and the stability of the epsilon algorithm
    • P. Wynn, On the convergence and the stability of the epsilon algorithm, SIAM J. Numer. Anal. 3 (1966) 91-122.
    • (1966) SIAM J. Numer. Anal. , vol.3 , pp. 91-122
    • Wynn, P.1
  • 118
    • 34250535763 scopus 로고
    • Upon systems of recursions which obtain among the quotients of the Padé table
    • P. Wynn, Upon systems of recursions which obtain among the quotients of the Padé table, Numer. Math. 8 (1966) 264-269.
    • (1966) Numer. Math. , vol.8 , pp. 264-269
    • Wynn, P.1
  • 119
    • 0005475356 scopus 로고
    • Strong interaction dynamics with Padé approximants
    • J. Zinn-Justin, Strong interaction dynamics with Padé approximants, Phys. Rep. 1 (1971) 55-102.
    • (1971) Phys. Rep. , vol.1 , pp. 55-102
    • Zinn-Justin, J.1


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