A criterion for the best approximation of constants by simple partial fractions (Q1947793)
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scientific article; zbMATH DE number 6158182
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A criterion for the best approximation of constants by simple partial fractions |
scientific article; zbMATH DE number 6158182 |
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A criterion for the best approximation of constants by simple partial fractions (English)
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26 April 2013
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A simple rational function is a sum of the reciprocals of \(n\) linear functions of the form \((x- x_i)\) defined on \([-1,1]\). This paper shows that, for sufficiently small numbers \(c\), the best approximation in the uniform norm to \(c\) by a simple rational function is characterized by the error function exhibiting \(n+1\) points of maximum amplitude but with alternating sign.
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approximation by sums of reciprocals of linear functions
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alternation characterization
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