Hyperinterpolation on the square (Q2475355)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Hyperinterpolation on the square |
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Hyperinterpolation on the square (English)
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11 March 2008
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The authors study a polynomial approximation algorithm which combines \textit{I. H. Sloan}'s hyperinterpolation procedure [J. Approximation Theory 83, No.~2, 238--254 (1995; Zbl 0839.41006)] with a near-minimal cubature formula for the product Chebyshev measure on the square. The Lebesgue constant of this approximation operator is estimated to grow no faster than a constant times the squared \(\log\) of the polynomial total degree. The algorithm is compared with two interpolation schemes and numerical tests are presented.
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hyperinterpolation
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square
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Xu points
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cubature formulas
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Lebesgue constant
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comparison of methods
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numerical examples
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algorithm
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Chebyshev measure
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