Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems

Numerische Mathematik

Volumn 84, Issue 3, 2000, Pages 497-518

  Scherer, Rudolf ^a   Schira, Thomas ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034407198     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050007     Document Type: Article

References (18)

1. Akrivis, G. (1984): Fehlerabschätzungen für Gauss-Quadraturformeln. Numer. Math. 44, 261-278
2. Brass, H. (1977): Quadraturverfahren. Vandenhoeck & Ruprecht, Göttingen
3. Brass, H., Schmeisser, G. (1979): The definiteness of Filippi's quadrature formulae and related problems. Internat. Ser. Numer. Math. 45, 109-119
4. Davis, P.J., Rabinowitz, P. (1984): Methods of numerical integration (Second edition). Academic Press Inc. (London)
5. -1 with complex a and some applications to certain non-Hermitian matrices. Approx. Theory and its Applic. 5, 15-31
6. Gautschi, W. (1991): On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures. Rocky Mountain J. Math. 21, 209-226. Corrected in Gautschi, W. (1991): Rocky Mountain J. Math. 21, 1143
7. Gautschi, W. (1992): Remainder estimates for analytic functions. Numerical Integration (Espelid, T.O., Genz, A. (eds.)). Kluwer Academic Publishers, pp. 133-145
8. Gautschi, W., Li, S. (1990): The remainer term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points. J. Comp. Appl. Math. 33, 315-329
9. Gautschi, W., Varga, R.S. (1983): Error bounds for Gaussian quadrature of analytic functions. SIAM J. Numer. Anal. 20, 1170-1186
10. Haussmann, W., Luik, E. (1989): Cubature remainder estimates by approximation degrees. Result. Math. 16, 212-227
11. Haussmann, W., Luik, E., Zeller, K. (1982): Cubature remainder and biorthogonal systems. Internat. Ser. Numer. Math. 61, 191-200
12. Krylov, V.I. (1962): Approximate calculation of integrals. ACM Monograph Series, Macmillan, New York
13. Luik, E. (1988): Quadrature errors and biorthogonality. Internat. Ser. Numer. Math. 85, 111-116
14. Nicholson, D., Rabinowitz, P., Richter, N., Zeilberger, D. (1971): On the error in the numerical integration of Chebyshev polynomials. Math. Comp. 25, 79-86
15. Schira, T. (1994): Ableitungsfreie Fehlerabschätzungen bei numerischer Integration holomorpher Funktionen. Ph.D. Dissertation, Universität Karlsruhe
16. Schira, T. (1997): The remainder term for analytic functions of symmetric Gaussian quadratures. Math. Comp. 66, 297-310
17. Schira, T. (1996): The remainder term for analytic functions of Gauss-Lobatto quadratures. J. Comp. Appl. Math. 76, 171-193
18. Szegö, G. (1975): Orthogonal polynomials (fourth edition). American Mathematical Society, Colloquium Publications 23, Providence, RI