Cubature Formulae and Polynomial Ideals
Copyright policy )Cubature Formulae and Polynomial Ideals
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.
- University of Oregon United States
- University of Oregon Eugene United States
variety, Cubature formula, polynomial ideal, Applied Mathematics, common zeros, Multidimensional problems, orthogonal polynomials in several variables, Numerical quadrature and cubature formulas, cubature formulae, Approximate quadratures
variety, Cubature formula, polynomial ideal, Applied Mathematics, common zeros, Multidimensional problems, orthogonal polynomials in several variables, Numerical quadrature and cubature formulas, cubature formulae, Approximate quadratures
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