Journal
NUMERICAL ALGORITHMS
Volume 66, Issue 3, Pages 525-553Publisher
SPRINGER
DOI: 10.1007/s11075-013-9747-2
Keywords
Multivariate orthogonal polynomials; Three term relations; Moment functionals
Categories
Funding
- MEC of Spain [MTM2012-36732-C03-02]
- Diputacion General de Aragon project [E-64]
- MICINN of Spain
- European Regional Development Fund (ERDF) [MTM2011-28952-C02-02]
- Junta de Andalucia [FQM-0229, P09-FQM-4643, P11-FQM-7276]
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Let {P-n}(n >= 0) and {Q(n)}(n >= 0) be two monic polynomial systems in several variables satisfying the linear structure relation Q(n) = P-n + MnPn-1, n >= 1, where M-n are constant matrices of proper size and Q(0) = P-0. The aim of our work is twofold. First, if both polynomial systems are orthogonal, characterize when that linear structure relation exists in terms of their moment functionals. Second, if one of the two polynomial systems is orthogonal, study when the other one is also orthogonal. Finally, some illustrative examples are presented.
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