Abstract
The authors give new error estimates of product quadrature formulae in weighted-L1 norm.
1990 Mathematics Subject Classification (1985 Revision).41A55.
This material is based upon work supported by the Ministero dell’Universitá e della Ricerca Scientifica e Tecnologica (first author) and by the Hungarian National Foundation for Scientific Research Grant N.1910 (second author).
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References
H. Braß: Quadraturverfahren, Vanclenhoeck and Ruprecht, Göttingen (1977).
G. Criscuolo and G. Mastroianni: A Bound for generalized Jacobi Functions of second kind, Calcolo, XXIV, II, (1987), 193–198.
G. Criscuolo and G. Mastroianni and P. Nevai: Associated Generalized Jacobi Functions and Polynomials, J. of Math. Anal. and Appl. 158, 1, (1991), 15–34.
R.A. De Vore and R. Scott: Error Bounds for Gaussian Quadrature and Weighted-L 1 Polynomial Approximation, SIAM J. Numer. Anal., 21, 2, (1984), 400–412.
Z. Ditzian, V. Totik: Moduli of smoothness S.C.M., Springer-Verlag, Berlin (1987).
T. Erdélyi and P. Nevai: Generalized Jacobi weights, Christoffel functions and zeros of orthogonal polynomials, J.Approx. Theory, (to appear).
T. Erdélyi: Remez-type inequalities and their applications (preprint).
K.J. Förster, K. Petras: On a Problem Proposed by H. Braß Concerning the Remainder Term in Quadrature for Convex Functions, Numer. Math. 57, (1990), 763–777.
G. Freud: Orthogonal Polynomials, AKADÉMIAI KIADÓ, Budapest (1971).
D. Lubinski and P. Nevai: Markov-Bernstein Inequalities Revised, A’p’prox. Theory and its Appl., 314, (1987), 98–118.
G. Mastroianni: Christoffel functions and error of positive quadrature formulae (manuscript).
P. Nevai: Mean Convergence of Lagrange Interpolation III, Trans. Amer. Math. Soc, 282, (1984), 669–698.
K. Petras: Asymptotic Behaviour of Peano Kernel of Fixed Order, Numerical Integration III (H. Braß, G. Hämmerlin eds.), ISNM 85, Birkhäuser Verlag, Basel (1988), 186–198.
K. Petras: Error Bounds for Gaussian and Related Quadrature and Application to R-Convex Functions, SIAM J. Numer. Anal, 29, 2, (1992), 578–585.
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© 1993 Springer Basel AG
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Mastroianni, G., Vértesi, P. (1993). Error Estimates of Product Quadrature Formulae. In: Brass, H., Hämmerlin, G. (eds) Numerical Integration IV. ISNM International Series of Numerical Mathematics, vol 112. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6338-4_19
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DOI: https://doi.org/10.1007/978-3-0348-6338-4_19
Publisher Name: Birkhäuser, Basel
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