On the existence of the best discrete approximation in \(l_p\) norm by reciprocals of real polynomials (Q1008718)
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scientific article; zbMATH DE number 5534946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the existence of the best discrete approximation in \(l_p\) norm by reciprocals of real polynomials |
scientific article; zbMATH DE number 5534946 |
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On the existence of the best discrete approximation in \(l_p\) norm by reciprocals of real polynomials (English)
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30 March 2009
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Consider the problem of approximation by reciprocals of polynomials with real coefficients. The author gives a condition on the data which is necessary and sufficient for the existence of the best \({ l_p}\) estimate. A sufficient condition for the existence of the best \({ l_p}\) estimate is presented. Special attention is given to a discrete least squares approximation by reciprocals of linear functions. Examples are provided to show that the solution may not exist and a best estimate may not be unique.
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reciprocals of polynomials
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data fitting
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discrete rational approximation
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existence problem.
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