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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Obtaining cubatures for rectangles and other planar regions by using orthogonal polynomials

Author: Richard Franke
Journal: Math. Comp. 25 (1971), 803-817
MSC: Primary 65D30
MathSciNet review: 0300440
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Abstract: A. H. Stroud has recently shown the existence of cubature formulas for planar regions which use ${m^2}$ points and have polynomial precision $2m - 1$. In this paper, the author gives sufficient conditions for the existence of formulaa using fewer than ${m^2}$ points, and having polynomial precision $2m - 1$. An algorithm is given for computing such formulas, and is shown to be useful in a more general setting than given in the theorem. Numerical examples are given, both in terms of previously known and new cubature formulas.

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Keywords: Approximate integration, cubature formula, orthogonal polynomials, algebraic function, common zeros, positive weights, polynomial precision, rectangles, planar regions
Article copyright: © Copyright 1971 American Mathematical Society