Cubature formulae and polynomial ideals (Q1970520)
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scientific article; zbMATH DE number 1420092
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cubature formulae and polynomial ideals |
scientific article; zbMATH DE number 1420092 |
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Cubature formulae and polynomial ideals (English)
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21 March 2000
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The main purpose of this paper is to study the structure of cubature formulae using the notion of a polynomial ideal and its variety. The author proves that if \(I\) is a polynomial ideal generated by a proper set of \((2n-1)\) orthogonal polynomials and if the cardinality of the variety \(V(I)\) is equal to the codimension of \(I\), then there exists a cubature formula of degree \(2n-1\) based on the points in the variety. The result generalizes Gaussian cubature formulae. This result also offers a new method for constructing cubature formulae.
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cubature formulae
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polynomial ideal
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0.92304194
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0.9075688
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0.89204943
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