A note on Lagrange interpolation of functions of generalized bounded variation

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1993 English Publisher:Springer Science and Business Media LLCJournal:Approximation Theory and its Applications, volume 9, pages 1-8 (issn: 1000-9221,

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Authors: Sun, Xiehua;

doi: 10.1007/bf02836245

A note on Lagrange interpolation of functions of generalized bounded variation

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Abstract

Summary: We solve a remainded problem posed by the author [Acta Math. Hung. 53, No. 1/2, 75-84 (1989; Zbl 0683.41001)], whether the following estimate approximation for the class \(f'\in C[-1,1]\cap BV\) by Lagrange interpolation based on the Jacobi abscissas: \(L^{(\alpha,\beta)}_ n(f,x)- f(x)= O(1/n)\) holds, if \(\alpha\neq\beta\alpha, \beta\geq -1\).

Related Organizations

China Jiliang University
China (People's Republic of)

Keywords

Jacobi polynomials, Lagrange interpolation, Interpolation in approximation theory, rate of convergence

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