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Cubature Formulae and Polynomial Ideals

✍ Scribed by Yuan Xu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
172 KB
Volume
23
Category
Article
ISSN
0196-8858

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✦ Synopsis

The structure of cubature formulae of degree 2 n y 1 is studied from a polynomial ideal point of view. The main result states that if I is a polynomial ideal Ε½ . generated by a proper set of 2 n y 1 -orthogonal polynomials and if the cardinality Ε½ . of the variety V I is equal to the codimension of I, then there exists a cubature formula of degree 2 n y 1 based on the points in the variety. The result covers a number of cubature formulae in the literature, including Gaussian cubature formulae on one end and the usual product formulae on the classical domains on the other end. The result also offers a new method for constructing cubature formulae.

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