On product integration with gauss-kronrod nodes

SIAM Journal on Numerical Analysis

Volumn 35, Issue 1, 1998, Pages 78-92

  Bhrich, Sven ^a  

^a UNIVERSITY OF HILDESHEIM   (Germany)

Author keywords

Convergence; Gauss Kronrod nodes; Product integration; Stability

Indexed keywords

EID: 0041728404     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036142995295790     Document Type: Article

References (28)

1. C.T.H. BAKER, The Numerical Treatment of Integral Equations, Clarendon Press, Oxford, 1978.
2. H. BRASS, Quadraturverfahren, Vandenhoeck & Ruprecht, Göttingen, 1977.
3. T.S. CHIHARA, An Introduction to the Theory of Orthogonal Polynomials, Gordon and Breach, New York, 1978.
4. C. DAGNINO, Extended product integration rules, BIT, 23 (1983), pp. 488-499.
5. P.J. DAVIS AND P. RABINOWITZ, Methods of Numerical Integration, Academic Press, New York, 1984.
6. S. EHRICH, Asymptotic properties of Stieltjes polynomials and Gauss-Kronrod quadrature formulae, J. Approx. Theory, 82 (1995), pp. 287-303.
7. S. EHRICH AND G. MASTROIANNI, Stieltjes polynomials and Lagrange interpolation, Math. Comp., 66 (1997), pp. 311-331.
8. G. FREUD, Orthogonale Polynome, Birkhäuser, Basel, 1969.
9. W. GAUTSCHI, Gauss-Kronrod Quadrature - A Survey, in Numerical Methods and Approximation Theory III, G.V. Milovanović, ed., Niš, (1988), pp. 39-66.
10. W. GAUTSCHI AND S.E. NOTARIS, An algebraic and numerical study of Gauss-Kronrod quadrature formulae for Jacobi weight functions, Math. Comp., 51 (1988), pp. 321-248.
11. G. MASTROIANNI, Uniform convergence of derivatives of Lagrange interpolation, J. Comput. Appl. Math., 43 (1992), pp. 37-51.
12. G. MONEGATO, A note on extended Gaussian quadrature rules, Math. Comp., 30 (1976), pp. 812-817.
13. G. MONEGATO, Positivity of weights of extended Gauss-Legendre quadrature rules, Math. Comp., 32 (1978), pp. 243-245.
14. G. MONEGATO, Stieltjes polynomials and related quadrature rules, SIAM Rev., 24 (1982), pp. 137-158.
15. G. MONEGATO, Orthogonal polynomials and product integration for one-dimensional Fredholm integral equations with "nasty" kernels, in Proc. 9th Conference on Problems and Methods in Mathematical Physics, Teubner-Texte Math. 111, Leipzig, (1989), pp. 185-192.
16. NUMERICAL ALGORITHMS GROUP FORTRAN LIBRARY, Mark 15, NAG Ltd., Oxford, UK, 1991.
17. F. PEHERSTORFER, On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas, J. Approx. Theory, 70 (1992), pp. 156-190.
18. R. PIESSENS, E. DEDONCKER, C. ÜBERHUBER, AND D.K. KAHANER, QUADPACK - A subroutine package for automatic integration, Springer Series in Computational Mathematics 1, Berlin, 1983.
19. P. RABINOWITZ, The convergence of interpolatory product integration rules, BIT, 26 (1986), pp. 131-134.
20. I.H. SLOAN, The numerical solution of Fredholm equations of the second kind by polynomial interpolation, J. Integral Equations, 2 (1980), pp. 265-279.
21. I.H. SLOAN, Analysis of general quadrature methods for integral equations of the second kind, Numer. Math., 38 (1981), pp. 263-278.
22. I.H. SLOAN AND W.E. SMITH, Product-integration with the Clenshaw-Curtis and related points. Convergence properties, Numer. Math., 3 (1978), pp. 415-428.
23. I.H. SLOAN AND W.E. SMITH, Product-integration with the Clenshaw-Curtis and related points. Implementation and error estimates, Numer. Math., 34 (1980), pp. 387-401.
24. I.H. SLOAN AND W.E. SMITH, Properties of interpolatory product integration rules, SIAM J. Numer. Anal., 19 (1982), pp. 427-442.
25. G. SZEGÖ, Über gewisse orthogonale Polynome, die zu einer oszillierenden Belegungsfunktion gehören, Math. Ann., 110 (1934), pp. 501-513.
26. G. SZEGÖ, Orthogonal Polynomials, AMS Colloq. Publishing 23, Providence, RI, 1975.
27. A.F. TIMAN, Theory of Approximation of Functions of a Real Variable, Dover, New York, 1994.
28. S. WOLFRAM, Mathematica. A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley, Reading, MA, 1991.