The computation of orthogonal rational functions on an interval

Journal of Computational and Applied Mathematics

Volumn 179, Issue 1-2 SPEC. ISS., 2005, Pages 355-373

  Van Deun, Joris ^a   Bultheel, Adhemar ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Orthogonal rational functions; Quadrature

Indexed keywords

ASYMPTOTIC STABILITY; CALCULATIONS; CONVERGENCE OF NUMERICAL METHODS; INTERPOLATION; MATHEMATICAL TRANSFORMATIONS; POLES AND ZEROS; POLYNOMIALS; THEOREM PROVING;

ERROR BOUNDS; ORTHOGONAL RATIONAL FUNCTIONS; QUADRATURE;

FUNCTIONS;

EID: 17744381777     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.09.050     Document Type: Article

References (15)

1. N.I. Achieser Theory of Approximation 1956 Frederick Ungar New York
2. A. Bultheel, P. González-Vera, E. Hendriksen, O. Njåstad, Orthogonal Rational Functions, Cambridge Monographs on Applied and Computational Mathematics, vol. 5, Cambridge University Press, Cambridge, 1999.
3. A. Bultheel P. González-Vera E. Hendriksen O. Njåstad Orthogonal rational functions and quadrature on the real half line J. Complexity 19 2003 212-230
4. A. Bultheel P. González-Vera E. Hendriksen O. Njåstad Orthogonal rational functions and tridiagonal matrices J. Comput. Appl. Math. 153 1-2 2003 89-97
5. P.J. Davis Interpolation and Approximation 1968 Blaisdell New York
6. W. Gautschi Construction of Gaussian-Christoffel quadrature formulas Math. Comput. 22 1968 251-270
7. W. Gautschi On the construction of Gaussian quadrature rules from modified moments Math. Comput. 24 1970 245-260
8. W. Gautschi, Orthogonal polynomials: Applications and computation. in: A. Iserles (Ed.), Acta Numerica, vol. 5, Cambridge University Press, Cambridge, 1996, pp. 45-119.
9. E.A. Rakhmanov On the asymptotics of the ratio of orthogonal polynomials, Math. USSR Sbornik 32 1977 199-213
10. W. Rudin Real and Complex Analysis 3rd ed. 1987 McGraw-Hill New York
11. J. Van Deun A. Bultheel Orthogonal rational functions and quadrature on an interval J. Comput. Appl. Math. 153 1-2 2003 487-495
12. J. Van Deun A. Bultheel Ratio asymptotics for orthogonal rational functions on an interval J. Approx. Theory 123 2003 162-172
13. J. Van Deun A. Bultheel An interpolation algorithm for orthogonal rational functions J. Comput. Appl. Math. 164-165 2004 749-762
14. J. Van Deun, A. Bultheel, A weak-star convergence result for orthogonal rational functions, J. Comput. Appl. Math. (2005), to appear.
15. J. Van Deun, A. Bultheel, P. González-Vera, Computing orthogonal rational functions with poles near the boundary, in preparation.