A kind of \(C^{n+k}\) polynomial interpolation with least-squares errors (Q2744361)
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scientific article; zbMATH DE number 1648941
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A kind of \(C^{n+k}\) polynomial interpolation with least-squares errors |
scientific article; zbMATH DE number 1648941 |
Statements
23 October 2002
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polynomial interpolation
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oscillation phenomenon
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least square error
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Runge phenomenon
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A kind of \(C^{n+k}\) polynomial interpolation with least-squares errors (English)
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The authors construct polynomials of degree \(n+k, k\geq 0\) fixed, which interpolate \(f\) at given \(n+1\) knots. In all such polynomials there exsits just one with least \(L_2\) error. Some properties of the best polynomial are established. By using these polynomials, the Runge phenomenon is restrained effectively.
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