A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations | Zendy

Marc Van Barel | Zendy; Andrey Chesnokov | Zendy

Open Access

A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations

Author(s) -

Marc Van Barel,

Andrey Chesnokov

Publication year - 2010

Publication title -

numerical algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.981

H-Index - 64

eISSN - 1572-9265

pISSN - 1017-1398

DOI - 10.1007/s11075-010-9392-y

Subject(s) - mathematics , recurrence relation , orthogonal polynomials , discrete orthogonal polynomials , classical orthogonal polynomials , orthonormal basis , bivariate analysis , gegenbauer polynomials , eigenvalues and eigenvectors , inverse , difference polynomials , product (mathematics) , combinatorics , statistics , physics , geometry , quantum mechanics

We present an algorithm computing recurrence relation coefficients for bivariate polynomials, orthonormal with respect to a discrete inner product. These polynomials make it possible to give the solution of a discrete least squares approximation problem. To compute these polynomials, we pose the inverse eigenvalue problem and solve it efficiently and in a stable way, using a sequence of Givens rotations. We also show how to generalize the algorithm for the case of polynomials in more variables. Several numerical experiments show the validity of the approach.

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