N-point Padé approximates to real-valued Stieltjes series with nonzero radii of convergence

Journal of Computational and Applied Mathematics

Volumn 75, Issue 2, 1996, Pages 259-280

  Tokarzewski, Stanisław ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

Bounds; Continued fractions; Effective conductivity; N point Pad approximants; Two phase composites

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; SET THEORY;

CONTINUED FRACTIONS; MONOTONE SEQUENCES; N POINT PADE APPROXIMANTS; REAL VALUED STIELTJES SERIES; TWO PHASE COMPOSITES;

APPROXIMATION THEORY;

EID: 0030286777     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00068-4     Document Type: Article

References (19)

1. G.A. Baker, Essentials of Padé Approximants (Academic Press, London, 1975).
2. G.A. Baker and P. Graves-Morris, Padé approximants. Part I: basic theory, in: Gian-Carlo Rota, Ed., Encyclopedia of Mathematics and its Applications, Vol. 13 (Addison-Wesley, London, 1981).
3. G.A. Baker and P. Graves-Morris, Padé approximants, Part II: extensions and applications, in: Gian-Carlo Rota, Ed., Encyclopedia of Mathematics and its Applications. Vol. 14 (Addison-Wesley, London, 1981).
4. D.J. Bergman, The dielectric constant of a composite material - a problem in classical physics, Phys. Report. C 43 (1978) 377-407.
5. A. Bultheel, Laurent Series and their Padé Approximants (Birkhäuser, Basel, 1987).
6. L. Casasús and P. González-Vera, Two-point Padé type approximants for Stieltjes functions, in: C. Brezinski, A. Draux, A.P. Magnus, P. Moroni and A. Ronveaux, Eds., Proc. Polinômes Ortogonaux et Applications, Bar-le-Duc, 1984, Lecture Notes in Math., Vol. 1171 (Springer, Berlin, 1985) 408-418.
7. J. Gilewicz, Approximants de Padé (Springer, Berlin, 1978).
8. K. Golden and G. Papanicolaou, Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys. 90 (1983) 473-491.
9. P. González-Vera and O. Njȧstad, Convergence of two-point Padé approximants to series of Stieltjes, J. Comput. Appl. Math. 32 (1990) 97-105.
10. W.B. Gragg, Truncation error bounds for T-fractions, in: E.W. Cheney, Ed., Approximation Theory III (Academic Press, New York, 1980) 455-460.
11. W.B. Jones, O. Njȧstad and W.J. Thron, Two-point Padé expansions for a family of analytic functions, J. Comput. Appl. Math. 9 (1983) 105-123.
12. W.B. Jones and W.J. Thron, A posterior bound for truncation error of continued fraction, SIAM J. Numer. Anal. 8 (1970) 693-705.
13. W.B. Jones and W.J. Thron, Continued fraction analytic theory and its applications, in: Gian-Carlo Rota, Ed., Encyclopedia of Mathematics and its Applications. Vol. II (Addison-Wesley, London, 1980).
14. R.C. McPhedran and G.W. Milton, Bounds and exact theories for the transport properties of inhomogeneous media, Appl. Phys. A 26 (1981) 207-220.
15. R.C. McPhedran, L. Poladian and G.W. Milton, Asymptotic studies of closely spaced highly conducting cylinders, Proc. R. Soc. London A 415 (1988) 185-196.
16. S. Tokarzewski, Two-point Padé approximants for the expansions of Stieltjes functions in real domain, J. Comput. Appl. Math. 67 (1996) 59-72.
17. S. Tokarzewski, J. Bławzdziewicz and I.V. Andrianov, Effective conductivity of densely packed highly conducting cylinders, Appl. Phys. A 59 (1994), 601-604.
18. S. Tokarzewski, J. Blawzdziewicz and I.V. Andrianov, Two-point Padé approximants for formal Stieltjes series, Numer. Algorithms 8 (1994), 313-328.
19. H.S. Wall, Analytic Theory of Continued Fractions (Van Nostrand, New York, 1948).