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

Authors:
Marc Barel;Andrey Chesnokov
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Heverlee, Belgium 3001;Department of Computer Science, Katholieke Universiteit Leuven, Heverlee, Belgium 3001
Venue:
Numerical Algorithms
Year:
2010

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Abstract

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.