# 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.

## Keywords

Uniform approximation levelling algorithm proximity map bolt.## Mathematics Subject Classifications:

41A30 41A65 46B28 65D15.## Notes

### Acknowledgement

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

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