Orthogonal rational functions and quadrature on the real half line

Journal of Complexity

Volumn 19, Issue 3, 2003, Pages 212-230

  Bultheel, A ^a   Gonzalez Vera P ^b   Hendriksen, E ^c   Njåstad, Olav ^d  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b UNIVERSIDAD DE LA LAGUNA   (Spain)

^c UNIVERSITY OF AMSTERDAM   (Netherlands)

^d NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037716331     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0885-064X(03)00002-5     Document Type: Article

References (18)

1. N.I. Achieser, Theory of Approximation, Frederick Ungar Publ. Co. New York, 1956.
2. B.D. Bojanov, D. Braess, N. Dyn, Generalized Gaussian quadrature formulas, J. Approx. Theory 48 (1986) 335-353.
3. A. Bultheel, C. Díaz-Mendoza, P. González-Vera, R. Orive, Quadrature on the half line and two-point Padé approximants to Stieltjes functions. Part III: The unbounded case, J. Comput. Appl. Math. 87 (1997) 95-117.
4. A. Bultheel, P. González-Vera, E. Hendriksen, O. Njådstad, Orthogonal Rational Functions, in: Cambridge Monographs on Applied and Computational Mathematics, Vol. 5, Cambridge University Press, Cambridge, 1999.
5. P.J. Davis, Interpolation and Approximation, Blaisdell, New York, 1963 (Reprint: Dover, New York, 1975).
6. A. Draux, Polynômes Orthogonaux Formels - Applications, in: Lecture Notes in Mathematics, Vol. 974, Springer, Berlin, 1983.
7. W. Gautschi, Gauss-type quadrature rules for rational functions, in: H. Brass, G. Hämmerlin (Eds.), Numerical Integration IV, Internat. Series of Numerical Mathematics, Vol. 112, Birkhäuser, Basel, 1993, pp. 111-130.
8. E. Hille, Analytic Function Theory, Vol. 2, Ginn and Co., Boston, 1962.
9. J. Illán, G. López-Lagomasino, A note on generalized quadrature formulas of Gauss-Jacobi type, in: Constructive Theory of Functions '84, Sofia, Publishing House of the Bulgarian Academy of Science, Sofia, 1984, pp. 513-518.
10. W.B. Jones, O. Njåstad, W.J. Thron, Two-point Padé expansions for a family of analytic functions, J. Comput. Appl. Math. 9 (1983) 105-124.
11. W.B. Jones, W.J. Thron, H. Waadeland, A strong Stieltjes moment problem, Trans. Amer. Math. Soc. 206 (1980) 503-528.
12. S. Karlin, W.J. Studden, Tchebycheff Systems: With Applications in Analysis and Statistics, Pure and Applied Mathematics, Vol. 15, Wiley Interscience, New York, 1966.
13. V.J. Krylov, Approximate Calculation of Integrals, MacMillan, New York, 1962.
14. G. López-Lagomasino, J. Illán-González, Quadrature formulas for unbounded intervals, Rev. Cienc. Mat. 3 (1982) 29-47 (in Spanish).
15. A.S. Ranga, Another quadrature rule of highest algebraic degree, Numer. Math. 28 (1994) 283-294.
16. A.H. Stroud, D. Secrest, Gaussian Quadrature Formulas, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Englewood Cliffs, NJ, 1966.
17. G. Szego, Orthogonal Polynomials, Amer. Math. Soc. Colloquium Publication, Vol. 33, American Mathematical Society, Providence, RI 3rd Edition, 1967, 1st Edition, 1939.
18. W. Van Assche, I. Vanherwegen, Quadrature formulas based on rational interpolation, Math. Comp. 16 (1993) 765-783.