Optimal Polynomial Prediction Measures and Extremal Polynomial Growth
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Publication:6331931
DOI10.1007/S00365-020-09522-1arXiv1912.12462MaRDI QIDQ6331931
Norm Levenberg, Len Bos, Joaquim Ortega-Cerdà
Publication date: 28 December 2019
Abstract: We show that the problem of finding the measure supported on a compact subset K of the complex plane such that the variance of the least squares predictor by polynomials of degree at most n at a point exterior to 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 this external point. We use this to find the polynomials of extremal growth for the interval [-1,1] at a purely imaginary point. The related problem on the extremal growth of real polynomials was studied by ErdH{o}s in 1947.
Approximation in the complex plane (30E10) Polynomials and rational functions of one complex variable (30C10) Inequalities in the complex plane (30A10)
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