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Article

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2020-11-02

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/181476

Optimal Polynomial Prediction Measures and Extremal Polynomial Growth

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https://doi.org/10.1007/s00365-020-09522-1

Abstract

We show that the problem of finding the measure supported on a compact set $K\subset \C$ such that the variance of the least squares predictor by polynomials of degree at most $n$ at a point $z_0\in\C^d\backslash K$ is a minimum, is equivalent to the problem of finding the polynomial of degree at most $n,$ bounded by 1 on $K,$ with extremal growth at $z_0.$ We use this to find the polynomials of extremal growth for $[-1,1]\subset \C$ at a purely imaginary point. The related problem on the extremal growth of real polynomials was studied by Erd\H{o}s (Bull Am Math Soc 53:1169-1176, 1947).

Subject

Desigualtats (Matemàtica), Teoria de l'aproximació, Funcions de variables complexes

Subject (English)

Inequalities (Mathematics), Approximation theory, Functions of complex variables

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

BOS, Leonard Peter, LEVENBERG, Norm and ORTEGA CERDÀ, Joaquim. Optimal Polynomial Prediction Measures and Extremal Polynomial Growth. Constructive Approximation. 2020. Vol. 54, num. 3, pags. 431-453. ISSN 0176-4276. [consulted: 18 of August of 2026]. Available at: https://hdl.handle.net/2445/181476

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