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.

中文翻译：

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最优多项式预测测度和极值多项式增长

我们表明，找到在复平面的紧致子集 K 上支持的测度的问题，使得最小二乘预测器在 K 外部的点处的阶数至多为 n 的多项式的方差最小，等价于问题找到最多 n 次的多项式，在 K 上以 1 为界，在这个外部点有极值增长。我们使用它来找到区间 [-1,1] 在纯虚点处的极值增长多项式。Erd\H{o}s 于 1947 年研究了实数多项式极值增长的相关问题。