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arXiv · 1912.12462

Optimal Polynomial Prediction Measures and Extremal Polynomial Growth

L. Bos·N. Levenberg·J. Ortega-Cerda
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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 Erd\H{o}s in 1947.

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L. Bos, N. Levenberg, J. Ortega-Cerda. 2019-12-28. Optimal Polynomial Prediction Measures and Extremal Polynomial Growth. https://doi.org/10.1007/s00365-020-09522-1

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