Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/181476
Title: | Optimal Polynomial Prediction Measures and Extremal Polynomial Growth |
Author: | Bos, Leonard Peter Levenberg, Norm Ortega Cerdà, Joaquim |
Keywords: | Desigualtats (Matemàtica) Teoria de l'aproximació Funcions de variables complexes Inequalities (Mathematics) Approximation theory Functions of complex variables |
Issue Date: | 2-Nov-2020 |
Publisher: | Springer Science + Business Media |
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). |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s00365-020-09522-1 |
It is part of: | Constructive Approximation, 2020, vol. 54, num. 3, p. 431-453 |
URI: | http://hdl.handle.net/2445/181476 |
Related resource: | https://doi.org/10.1007/s00365-020-09522-1 |
ISSN: | 0176-4276 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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