Two-point Padé approximants for the expansions of Stieltjes functions in real domain

Journal of Computational and Applied Mathematics

Volumn 67, Issue 1, 1996, Pages 59-72

  Tokarzewski, Stanisław ^a  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

Continued fractions; Effective conductivity; Two point Pad approximants

Indexed keywords

CALCULATIONS; COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS;

CONTINUED FRACTIONS; EFFECTIVE CONDUCTIVITY; STIELTJES FUNCTIONS; TRANSPORT COEFFICIENTS; TWO POINT PADE APPROXIMANTS;

APPROXIMATION THEORY;

EID: 0030078930     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(94)00122-7     Document Type: Article

References (18)

1. G.A. Baker, Essentials of Padé Approximants (Academic Press, New York, 1975).
2. G.A. Baker and P. Graves-Morris, Padé approximants, part I: Basic theory, in: G.-C. Rota, Ed., Encyclopedia of Mathematics and its Applications, Vol. 13 (Addison-Wesley, Reading, MA, 1981).
3. G.A. Baker and P. Graves-Morris, Padé approximants, part II: Extensions and applications, in: G.-C. Rota, Ed., Encyclopedia of Mathematics and its Applications, Vol. 14 (Addison-Wesley, Reading, MA, 1981).
4. D.J. Bergman, The dielectric constant of a composite material - a problem in classical physics, Phys. Rep. 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. Maroni 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. P. González-Vera and O. Njåstad, Convergence of two-point Padé approximants to series of Stieltjes, J. Comput. Appl. Math. 32 (1990) 97-105.
9. W.B. Gragg, Truncation error bounds for T-fractions, in: E.W. Cheney, Ed., Approximation Theory III (Academic Press, New York, 1980) 455-460.
10. W.B. Jones, O. Njåstad and W.J. Thron, Two-point Padé expansions for a family of analytic functions, J. Comput. Appl. Math. 9 (1983) 105-123.
11. W.B. Jones and W.J. Thron, A posteriori bound for truncation error of continued fractions, SIAM J. Numer. Anal. 8 (1970) 693-705.
12. W.B. Jones and W.J. Thron, Continued fractions: Analytic theory and its applications, in: G.-C. Rota, Ed., Encyclopedia of Mathematics and its Applications, Vol. 11 (Addison-Wesley, Reading, MA, 1980).
13. S. May, S. Tokarzewski, A. Zachara and B. Cichocki, Continued fraction representation for the effective thermal conductivity coefficient of a periodic two component composite, Internat. J. Heat Mass Transf. 37 (1994) 2165-2173.
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. Roy. Soc. London Ser. A 415 (1988) 185-196.
16. S. Tokarzewski, J. Blawzdziewicz and I.V. Andrianov, Two-point Padé approximants for Stieltjes series, IFTR Report 30/1993.
17. S. Tokarzewski, J. Blawzdziewicz and I.V. Andrianov, Effective conductivity of densely packed highly conducting cylinders, Appl. Phys. A 59 (1994) 601-604.
18. H.S. Wall, Analytic Theory of Continued Fractions (Van Nostrand, New York, 1948).