Best one-sided approximation to the Heaviside and sign functions

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• 作者：Jorge Bustamante^a ; José ; M. Quesada^b ; ^{jquesada@ujaen.es} ; Reinaldo Mart&#237 ; nez-Cruz^a
• 关键词：One-sided approximation ; Jacobi polynomials ; Hermite interpolation
• 刊名：Journal of Approximation Theory
• 出版年：2012
• 期刊代码：71_00219045
• 类别：mt
• 出版时间：June, 2012
• 卷：164
• 期：6
• 页码：791-802
• 文件大小：203 K

摘要

We find the polynomials of the best one-sided approximation to the Heaviside and sign functions. The polynomials are obtained by Hermite interpolation at the zeros of some Jacobi polynomials. Also we give an estimate of the error of approximation and characterize the extremal points of the convex set of the best approximants.