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Diliberto–Straus algorithm for the uniform approximation by a sum of two algebras

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Abstract

In 1951, Diliberto and Straus [5] proposed a levelling algorithm for the uniform approximation of a bivariate function, defined on a rectangle with sides parallel to the coordinate axes, by sums of univariate functions. In the current paper, we consider the problem of approximation of a continuous function defined on a compact Hausdorff space by a sum of two closed algebras containing constants. Under reasonable assumptions, we show the convergence of the Diliberto–Straus algorithm. For the approximation by sums of univariate functions, it follows that Diliberto–Straus’s original result holds for a large class of compact convex sets.

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Acknowledgement

The authors are grateful to the referee for numerous comments and suggestions that improved the original manuscript.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Az-1141, Baku, Azerbaijan

    AIDA KH ASGAROVA & VUGAR E ISMAILOV

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  1. AIDA KH ASGAROVA
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  2. VUGAR E ISMAILOV
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Correspondence to VUGAR E ISMAILOV.

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Communicating Editor: T S S R K Rao

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ASGAROVA, A.K., ISMAILOV, V.E. Diliberto–Straus algorithm for the uniform approximation by a sum of two algebras. Proc Math Sci 127, 361–374 (2017). https://doi.org/10.1007/s12044-017-0337-4

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  • DOI: https://doi.org/10.1007/s12044-017-0337-4

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