Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation (Q1015793)
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scientific article; zbMATH DE number 5550285
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation |
scientific article; zbMATH DE number 5550285 |
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Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation (English)
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30 April 2009
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Consider the approximation of a given function analytic in \((-1,1)\) by a \(N\)th degree polynomial that is chosen to minimize the least squares error at \(P\) equidistant points in the interval \([-1,1]\). Numerical evidence is presented that indicates that the Runge phenomenon which is present in the case \(P = N+1\) can be weakened, but not completely eliminated, for \(P \gg N+1\).
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interpolation
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Chebyshev interpolation
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least squares approximation
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polynomial approximation
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divergence
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