The convergence of diagonal Padé approximants and the Padé Conjecture

Journal of Computational and Applied Mathematics

Volumn 86, Issue 1, 1997, Pages 287-296

  Stahl, Herbert ^a  

^a BEUTH UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

Baker Gammel Wills Conjecture; Convergence in capacity; Pad approximation; Pad Conjecture; Spurious poles

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; POLES AND ZEROS;

PADE APPROXIMATION; PADE CONJECTURE; SPURIOUS POLES;

APPROXIMATION THEORY;

EID: 0031272505     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00162-3     Document Type: Article

References (24)

1. 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.
2. G.A. Baker Jr., P. Graves-Morris, Padé Approximants, Cambridge University Press, Cambridge, 1996.
3. S. Dumas, Sur le dévelopement des fonctions elliptiques en fractions continues, Thèse, Faculté de Philosophie, University of Zürich, 1908.
4. 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.
5. 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.
6. W.B. Gragg, The Padé table and its relation to certain algorithms of numerical analysis, SIAM Rev. 14 (1972) 1-62.
7. N.S. Landkof, Foundations of Modern Potential Theory, Springer, Berlin, 1972.
8. D.S. Lubinsky, Divergence of complex rational approximants, Pacific J. Math. 108 (1983) 141-153.
9. D.S. Lubinsky, Spurious poles in diagonal rational approximation, in: A.A. Gonchar, E.B. Saff (Eds.), Progress in Approximation Theory, Springer, Berlin, 1992, pp. 191-213.
10. D.S. Lubinsky, Convergence of diagonal Padé approximants for functions analytic near 0, Trans. Amer. Math. Soc. 347 (1995) 3149-3157.
11. D.S. Lubinsky, E.B. Saff, Convergence of Padé approximants of partial theta functions and Rogers-Szegö polynomials, Constr. Approx. 3 (1987) 331-361.
12. B. Meyer, On convergence in capacity, Bull. Austral. Math. Soc. 14 (1976) 1-5.
13. J. Nuttall, The convergence of Padé approximants of meromorphic functions, J. Math. Anal. Appl. 31 (1970) 129-140.
14. J. Nuttall, Asymptotics of diagonal Hermite-Padé polynomials, J. Approx. Theory 42 (1984) 299-386.
15. O. Perron, Kettenbrüche, Chelsea, 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. H. Stahl, Divergence of diagonal Padé approximants and the asymptotic behavior of orthogonal polynomials associated with nonpositive measures, Constr. Approx. 1 (1985) 249-270.
19. H. Stahl, On the convergence of generalized Padé approximants, Constr. Approx. 5 (1989) 221-240.
20. H. Stahl, The convergence of Padé approximants to functions with branch points, J. Approx. Theory (1997/1998) in press.
21. H. Stahl, Diagonal Padé approximants to hyperelliptic functions, Ann. Fac. Sci. Toulouse, to appear.
22. H. Stahl, V. Totik, General Orthogonal Polynomials, Cambridge University Press, Cambridge, 1992.
23. M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo, 1959.
24. H. Wallin, The convergence of Padé approximants and the size of the power series coefficients, Appl. Anal. 4 (1974) 235-251.