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

作者：Van Barel Marc^*; Chesnokov Andrey

来源：Numerical Algorithms, 2010, 55(2-3): 383-402.

DOI：10.1007/s11075-010-9392-y

• Orthogonal polynomials
• Recurrence relations
• Unitary transformations
• Givens rotations
• Discrete least squares problem
• Bivariate interpolation and approximation
• Padua points

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.

• 出版日期2010-11