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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Recurrence formulas for multivariate orthogonal polynomials


Author: Yuan Xu
Journal: Math. Comp. 62 (1994), 687-702
MSC: Primary 42C05; Secondary 65D30
MathSciNet review: 1212269
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Abstract: In this paper, necessary and sufficient conditions are given so that multivariate orthogonal polynomials can be generated by a recurrence formula. As a consequence, orthogonal polynomials of total degree n in d variables that have $ \dim \Pi _n^d$ common zeros can now be constructed recursively. The result is important to the construction of Gaussian cubature formulas.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1212269-X
PII: S 0025-5718(1994)1212269-X
Keywords: Multivariate orthogonal polynomials, recurrence formula, three-term relation, common zeros of multivariate orthogonal polynomials, Gaussian cubature
Article copyright: © Copyright 1994 American Mathematical Society