\(\sigma\)-perfect splines and their application to optimal recovery problems (Q1824125)
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scientific article; zbMATH DE number 4117138
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\sigma\)-perfect splines and their application to optimal recovery problems |
scientific article; zbMATH DE number 4117138 |
Statements
\(\sigma\)-perfect splines and their application to optimal recovery problems (English)
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1987
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The author discusses applications of the \(\sigma\)-perfect splines to some problems related to the best recovery of a given functional on the basis of a partial information. A complete characterization of the Favard interpolation problem in \(W^ r_ q(a,b)\) \((1<q<\infty)\) for Birkhoff- type interpolation data is given. The best interpolant is a \(\sigma\)- perfect spline provided all but one of the preassigned values are equal to zero. Best recovery schemes with boundary values and the optimal differentiation schemes are also discussed.
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optimal recovery
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sigma-perfect splines
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applications
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Favard interpolation problem
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Birkhoff-type interpolation
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optimal differentiation schemes
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