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Equioscillation theorem : ウィキペディア英語版
Equioscillation theorem

The equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attributed to Chebyshev.
== Statement ==
Let f be a continuous function from () to \mathbf. Among all the polynomials of degree \le n, the polynomial g minimizes the uniform norm of the difference || f - g || _\infty if and only if there are n+2 points a \le x_0 < x_1 < \cdots < x_ \le b such that f(x_i) - g(x_i) = \sigma (-1)^i || f - g || _\infty where \sigma = \pm 1.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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