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TW 554
Marc Van Barel, Andrey ChesnokovA method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations
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.
report.pdf (350K) / mailto: M. Van Barel