Uniform approximation by discrete least squares polynomials

We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number o...

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Bibliographic Details
Published in:Journal of approximation theory 2008-05, Vol.152 (1), p.82-100
Main Authors: Calvi, Jean-Paul, Levenberg, Norman
Format: Article
Language:English
Subjects:
Discrete least squares
Markov's inequality
Polynomial approximation
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Summary:We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximants. For analytic functions, similar results may be achieved on more general K by allowing the number of points to grow at a slightly larger rate.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2007.05.005