A remark on best \(L^ 1\)-approximation by polynomials (Q910634)
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scientific article; zbMATH DE number 4140443
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on best \(L^ 1\)-approximation by polynomials |
scientific article; zbMATH DE number 4140443 |
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A remark on best \(L^ 1\)-approximation by polynomials (English)
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1988
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The integral \(\int^{1}_{-1}f(t)sgn U_ n(t)dt\), where \(U_ n(t)\) is the Chebyshev polynomial of the second kind, plays an important role in the \(L^ 1\)-approximation of f. The author shows that this integral is easy to evaluate if the expansion of f in terms of \(U_ n\) is known.
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Chebyshev polynomial of the second kind
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0.9660785
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0.9613354
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0.94316965
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0.93777215
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0.9278927
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0.92726153
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