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Erdös-Turán mean convergence theorem for Lagrange interpolation at Lobatto points

Published online by Cambridge University Press:  17 April 2009

William E. Smith
William E. Smith
Affiliation:
Department of Applied Mathematics, University of New South Wales, kensington 2033, Australia.
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Abstract

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Let {Qn} denote the orthogonal polynomials associated with the weight function p on [−1, 1] and let denote the zeros of (1−x2) Qn (x). Consider the Lagrange polynomials which interpolate a given continuous function at these points. It is shown that, as n → ∞, the Lagrange polynomial converges to the function in the W weighted mean square sense, where w (x) = ρ(x)\(1−x2), provided that W is integrable. An application to numerical product integration is noted.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 375 - 381
Copyright
Copyright © Australian Mathematical Society 1986

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