Obtaining cubatures for rectangles and other planar regions by using orthogonal polynomials
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- by Richard Franke PDF
- Math. Comp. 25 (1971), 803-817 Request permission
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.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 803-817
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1971-0300440-5
- MathSciNet review: 0300440