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Convergence of a quadrature formula for variable-signed weight functions

Published online by Cambridge University Press:  17 April 2009

H.S. Jung  and
K.H. Kwon
H.S. Jung
Affiliation:
Department of MathematicsKAIST373–1 Kusong-dong, Yusong-kuTaejon 305–701Korea e-mail: khkwon@jacobi.kaist.ac.kr
K.H. Kwon
Affiliation:
Department of MathematicsKAIST373–1 Kusong-dong, Yusong-kuTaejon 305–701Korea e-mail: khkwon@jacobi.kaist.ac.kr
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Abstract

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A quadrature formula for a variable-signed weight function w(x) is constructed using Hermite interpolating polynomials. We show its mean and quadratic mean convergence. We also discuss the rate of convergence in terms of the modulus of continuity for higher order derivatives with respect to the sup norm.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 275 - 288
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Balazs, K. and Kilgore, T., ‘On the simultaneous approximation of derivatives by Lagrange and Hermite interpolation’, J. Approx. Theory 60 (1990), 231–244.CrossRefGoogle Scholar
[2]Davis, P.J., Interpolation and approximation (Blaisdell, New York, 1963).Google Scholar
[3]Freud, G., Orthogonal polynomials (Pergamon Press, Oxford, 1971).Google Scholar
[4]Gautschi, W., ‘A survey of Gauss – Christoffel quadrature formula’, in E.B. Christoffel Symp., (Butzer, P.L. and Fehér, F., Editors) (Birkhäuser, Basel, 1981), pp. 72–147.CrossRefGoogle Scholar
[5]Gopengauz, I.E., ‘On a theorem of A.F. Timan on approximation of function by polynomials on a finite interval’, (in Russian) 1967, Mat. Zametki 1 (), 163–172; (English translation, Math. Notes I (1967), 110–116).Google Scholar
[6]Mastroianni, G. and Nevai, P., ‘Mean convergence of derivatives of Lagrange interpolation’, J. Comput. Appl. Math. 34 (1991), 385–396.CrossRefGoogle Scholar
[7]Nevai, P., ‘Mean convergence of Lagrange interpolation, III’, Trans. Amer. Math. Soc. 282 (1984), 669–698.CrossRefGoogle Scholar
[8]Struble, G.W., Orthogonal polynomials: Variable – signed weight functions, Ph.D. Thesis (University of Wisconsin, 1961).Google Scholar
[9]Vértesi, P. and Xu, Y., ‘Truncated Hermite interpolation polynomials’, Studia Sci. Math. Hungar. 23 (1993), 205–213.Google Scholar