Orthogonal rational functions and interpolatory product rules on the unit circle. ill: Convergence of general sequences

Analysis (Germany)

Volumn 20, Issue 2, 2000, Pages 99-120

  Bultheel, A ^a   Gonzalez Vera, P ^b   Hendriksen, E ^c   Njastad O ^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

multipoint Pad approximants; numerical quadrature; orthogonal rational functions

Indexed keywords

EID: 0012917997     PISSN: 01744747     EISSN: 21966753     Source Type: Journal    
DOI: 10.1524/anly.2000.20.2.99     Document Type: Article

References (17)

1. N.I. Akhiezer. The classical moment problem. Oliver and Boyd, Edinburgh, 1969. Originally published Moscow, 1961.
2. A. Bultheel, C. Diaz-Mendoza, P. Gonzalez-Vera, and R. Orive. Quadrature on the half line and two-point Pade approximants to Stieltjes functions. Part II: Convergence. J. Comput. Appl. Math., 77:53–76, 1997.
3. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Orthogonality and quadrature on the unit circle. In C. Brezinski, L. Gori, and A. Ronveaux, editors, Orthogonal Polynomials and their Applications, volume 9 of IM ACS annals on computing and applied mathematics, pages 205–210, Basel, 1991. J.C. Baltzer AG.
4. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Quadrature formulas on the unit circle and two-point Pade approximation. In A.M. Cuyt, editor, Nonlinear Numerical Methods and Rational Approximation II, pages 303–318. Kluwer, 1994.
5. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Quadrature formulas on the unit circle based on rational functions. J. Comput. Appl. Math., 50:159–170, 1994.
6. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. On the convergence of multipoint Pade-type approximants and quadrature formulas associated with the unit circle. Numer. Algorithms, 13:321–344, 1996.
7. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Rates of convergence of multipoint rational approximants and quadrature formulas on the unit circle. J. Comput. Appl Math., 77:77–102, 1997.
8. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Orthogonal rational functions and interpolatory product rules on the unit circle. I. Recurrence and interpolation. Analysis, 18:167–183, 1998.
9. A. Bultheel, P. Gonzalez-Vera, E. Hendriksen, and O. Njastad. Orthogonal rational functions and interpolatory product rules on the unit circle. II. Quadrature and convergence. Analysis, 18:185–200, 1998.
10. G. Freud. Orthogonal polynomials. Pergamon Press, Oxford, 1971.
11. W.B. Jones, O. Njastad, and W.J. Thron. Moment theory, orthogonal polynomials, quadrature and continued fractions associated with the unit circle. Bull. London Math. Soc., 21:113–152, 1989.
12. O. Njastad. Laurent polynomials and Gaussian quadrature. In T. Havie, editor, Romberg seminar on quadrature, interpolation, extrapolation and rational approximants, Det Kongelige Norske Videnskabers Selskab Skrifter (No. 2), pages 102–120, 1989.
13. I.H. Sloan and W.E. Smith. Properties of interpolatory product rules. SIAM J. Numer. Anal., 19:427–442, 1982.
14. H. Stahl and V. Totik. General orthogonal polynomials. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1992.
15. J. Szabados and P. Vertesi. A survey on mean convergence of interpolatory process. J. Comput. Appl. Math., 43:3–18, 1992.
16. G. Szego. Orthogonal polynomials, volume 33 of Amer. Math. Soc. Colloq. Publ. Amer. Math. Soc., Providence, Rhode Island, 3rd edition, 1967. First edition 1939.
17. W.J. Thron. L-polynomials orthogonal on the unit circle. In A.M. Cuyt, editor, Nonlinear Numerical Methods and Rational Approximation, pages 271–278. Kluwer, 1988.