Spurious poles in Padé approximation

Journal of Computational and Applied Mathematics

Volumn 99, Issue 1-2, 1998, Pages 511-527

  Stahl, Herbert ^a  

^a BEUTH UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

Approximation; spurious poles; Convergence of Pad approximants; Pad

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; POLES AND ZEROS;

PADE APPROXIMATION; SPURIOUS POLES;

APPROXIMATION THEORY;

EID: 0032207667     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00180-0     Document Type: Article

References (25)

1. N.I. Achiezer, Othogonal polynomials on several intervals, Dokl. Akad. Nauk. CCCP 134 (1960) 9-12; English transl. Soviet Math. Dokl. 1 (1961) 989-992.
2. N.I. Achiezer, Othogonal polynomials on several intervals, Dokl. Akad. Nauk. CCCP 134 (1960) 9-12; English transl. Soviet Math. Dokl. 1 (1961) 989-992.
3. G.A. Baker, Jr., J.L. Gammel, J.G. Wills, An investigation of the applicability of the Padé approximant method, J. Math. Anal. Appl. 2 (1961) 405-418.
4. G.A. Baker, Jr., P. Graves-Morris, Padé Approximants, Cambridge University Press, Cambridge, 1996.
5. J. Gilewicz, Approximants de Padé, Lecture Notes in Mathematics, vol. 667, Springer, Heidelberg, 1978.
6. J. Gilewicz, M. Pindor, Padé approximants and noise: The case of geometric series, Technical report, Centre de Physique Théoretique, Marseille, 1997.
7. A.A Gonchar, A local condition for single-valuedness of analytic functions, Mat. Sbornik 89 (131) (1972); English transl. in Math. USSR Sb. 18 (1972) 151-167.
8. A.A Gonchar, A local condition for single-valuedness of analytic functions, Mat. Sbornik 89 (131) (1972); English transl. in Math. USSR Sb. 18 (1972) 151-167.
9. A.A. Gonchar, E.A. Rakhamanov, Equilibrium distributions and degree of rational approximation of analytic functions, Mat. Sb. 134 (1987); English transl. in Math. USSR Sb. 62 (1989) 305-348.
10. A.A. Gonchar, E.A. Rakhamanov, Equilibrium distributions and degree of rational approximation of analytic functions, Mat. Sb. 134 (1987); English transl. in Math. USSR Sb. 62 (1989) 305-348.
11. N.S. Landkof, Foundations of Modern Potential Theory, Springer, Berlin, 1972.
12. D.S. Lubinsky, Divergence of complex rational approximants, Pacific J. Math. 108 (1983) 141-153.
13. B. Meyer, On convergence in capacity, Bull. Austral. Math. Soc. 14 (1976) 1-5.
14. J. Nuttall, The convergence of Padé approximants of meromorphic functions, J. Math. Anal. Appl. 31 (1970) 129-140.
15. O. Perron, Kettenbrüche, Chelsea Publ. Comp., New York, 1929.
16. Ch. Pommerenke, Padé approximants and convergence in capacity, J. Math. Anal. Appl. 41 (1973) 775-780.
17. E. A. Rakhmanov, On the convergence of Padé approximants in classes of holomorphic functions, Math. USSR Sb. 40 (1980) 149-155.
18. Th. Ransford, Potential Theory in the Complex Plane, Cambridge University Press, Cambridge, 1995.
19. E. Saff, V. Totik, Logarithmic Potentials with External Fields, Springer, Heidelberg, 1997.
20. H. Stahl, On the divergence of certain Padé approximants and the behavior of the associated orthogonal polynomials, in: 'Polynômes Orthogonaux et Applications', Lecture Notes in Mathematics, vol. 1171, Springer, Heidelberg, 1983, pp. 321-330.
21. H. Stahl, Divergence of diagonal Padé approximants and the asymptotic behavior of orthogonal polynomials associated with nonpositive measures, Constr. Approx. 1 (1985) 249-270.
22. H. Stahl, Diagonal Padé approximants to hyperelliptic functions, Annales de la Faculté des Sciences de Toulouse, no spécial Stieltjes, 1996, pp. 121-193.
23. H. Stahl, The convergence of Padé approximants to functions with branch points, J. Approx. Theory 91 (1997) 139-204.
24. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. vol. 23, Providence, RI, 1939.
25. W. Van Assche, Asymptotics for Orthogonal Polynomials, Lecture Notes in Mathematics, vol. 1265, Springer, Heidelberg, 1988.