Quadrature on the half-line and two-point Padé approximants to Stieltjes functions - II: Convergence

Journal of Computational and Applied Mathematics

Volumn 77, Issue 1-2, 1997, Pages 53-76

  Bultheel, A ^a   Diaz Mendoza, C ^b   Gonzalez Vera P ^b   Orive, R ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSIDAD DE LA LAGUNA   (Spain)

Author keywords

Orthogonal Laurent polynomials; Quadrature formula; Stieltjes function; Two point Pad approximation

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL TRANSFORMATIONS; POLYNOMIALS;

CAUCHY TRANSFORMS; ORTHOGONAL LAURENT POLYNOMIALS; QUADRATURE FORMULA; STIELTJES FUNCTION; TWO POINT PADE APPROXIMATION;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0030785278     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00122-7     Document Type: Article

References (22)

1. E. Alden, A survey of weak and strong moment problems with generalizations, Tech. Report, Dept. Math. Umeå, 1985.
2. C.M. Bonan-Hamada, W.B. Jones, W.J. Thron and A. Magnus, Para-orthogonal Laurent polynomials and associated sequences of rational functions, Numer. Algorithms 3 (1992) 67-74.
3. A. Bultheel, P. González-Vera and R. Orive, Quadrature on the half line and two-point Padé approximants to Stieltjes functions. Part I: Algebraic aspects. J. Comput. Appl. Math. 65 (1996) 57-72.
4. E.W. Cheney, Introduction to Approximation Theory (McGraw-Hill, New York, 1966).
5. C. Díaz-Mendoza, P. Gonzâlez-Vera and R. Orive, On convergence of two-point Padé-type approximants, Numer. Math. 72 (1996) 295-312.
6. A. Draux, Polynômes Orthogonaux Formels - Applications, Lecture Notes in Math., 974 (Springer, Berlin, 1983).
7. G. Freud, Orthogonal Polynomials (Pergamon Press, Oxford, 1971).
8. A.A. Gonchar and E.A. Rakhmanov, Equilibrium measure and the distribution of zeros of extremal polynomials, Math. USSR-Sb. 53 (1986) 119-130.
9. P. González-Vera, M. Jiménez-Páiz, G. López-Lagomasino and R. Orive, On the convergence of quadrature formulas connected with multipoint Padé-type approximants, J. Math. Anal. Appl. 202 (1996) 747-775.
10. P. González-Vera and O. Njåstad, Convergence of two-point Padé approximants to series of Stieltjes, J. Comput. Appl. Math. 32 (1990) 97-105.
11. E. Hille, Analytic Function Theory, Vol. 2 (Ginn and Co., Boston, 1962).
12. 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) 105-124.
13. W.B. Jones, W.J. Thron and H. Waadeland, A strong Stieltjes moment problem, Trans. Amer. Math. Soc. 206 (1980) 503-528.
14. V.J. Krylov, Approximate Calculation of Integrals (MacMillan, New York, 1962).
15. N.S. Landkof, Foundations of Modern Potential Theory (Springer, New York, 1972).
16. G. López-Lagomasino and A.M. Finkelshtein, Rate of convergence of two-point Padé approximants and logarithmic asymptotics of Laurent-type orthogonal polynomials, Constr. Approx. 11 (1995) 255-286.
17. O. Njåstad, Laurent polynomials and Gaussian quadrature, in: T. Håvie, Ed., Romberg Seminar on Quadrature, Interpolation, Extrapolation and Rational Approximants, Det Kongelige Norske Videnskabers Selskab Skrifter (No. 2) (1989) 102-120.
18. O. Njåstad and W.J. Thron, The theory of sequences of orthogonal L-polynomials, in: H. Waadeland and H. Wallin, Eds., Padé Approximants and Continued Fractions, Det Kongelige Norske Videnskabers Selskab Skrifter (No. 1) (1983) 54-91.
19. E.A. Rakhmanov and A.A. Gonchar, Equilibrium distributions and degree of rational approximation of analytic functions, Math. USSR-Sb. 62 (1989) 305-348.
20. I.H. Sloan and W.E. Smith, Properties of interpolatory product rules, SIAM J. Numer. Anal. 19 (1982) 427-442.
21. H. Stahl and V. Totik, General Orthogonal Polynomials, Encyclopedia of Mathematics and its Applications (Cambridge Univ. Press, Cambridge, 1992).
22. G. Szego, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 33 (Amer. Math. Soc., Providence, RIs, 3rd ed., 1967; 1st ed., 1939).