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On the Diliberto-Straus algorithm for the uniform approximation by a sum\n of two algebras

2016/03/23 by Aida Kh. Asgarova, Asgarova, Aida Kh., Vugar E. Ismailov +1
Computer Science · Mathematics · #41A30 #41A65 #46B28 #65D15 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1603.07073

openalex publication_date 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1951, Diliberto and Straus proposed a levelling algorithm for the uniform\napproximation of a bivariate function, defined on a rectangle with sides\nparallel to the coordinate axes, by sums of univariate functions. In the\ncurrent paper, we consider the problem of approximation of a continuous\nfunction defined on a compact Hausdorff space by a sum of two closed algebras\ncontaining constants. Under reasonable assumptions, we show the convergence of\nthe Diliberto-Straus algorithm. For the approximation by sums of univariate\nfunctions, it follows that Diliberto-Straus's original result holds for a large\nclass of compact convex sets.\n

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