Orthogonal polyanalytic polynomials and normal matrices
Mathematics of Computation
An Algorithm Based on Orthogonal Polynominal Vectors for Toeplitz Least Squares Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Orthogonal basis functions in discrete least-squares rational approximation
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Generalizations of orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Eigenvalue computation for unitary rank structured matrices
Journal of Computational and Applied Mathematics
Unitary rank structured matrices
Journal of Computational and Applied Mathematics
Generalizations of orthogonal polynomials
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
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We describe an algorithm for complex discrete least squares approximation, which turns out to be very efficient when function values are prescribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Rutishauser, Gragg, Harrod, Reichel, Ammar, and others. The underlying reason for efficiency is the existence of a recurrence relation for orthogonal polynomials, which are used to represent the solution. We show how these ideas can be generalized to least squares approximation problems of a more general nature.