Solving Toeplitz least-squares problems via discrete polynomial least-squares approximation at roots of unity

Marc Van Barel; Georg Heinig; Peter Kravanja

doi:10.1117/12.406493

13 November 2000 Solving Toeplitz least-squares problems via discrete polynomial least-squares approximation at roots of unity

Marc Van Barel, Georg Heinig, Peter Kravanja

Author Affiliations +

Proceedings Volume 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X; (2000) https://doi.org/10.1117/12.406493
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

Abstract

We present an algorithm for solving Toeplitz least squares problems. By embedding the Toeplitz matrix into a circulant block matrix and by applying the Discrete Fourier Transform, we are able to transform the linear least squares problem into a discrete least squares approximation problem for polynomial vectors. We have implemented our algorithm in Matlab. Numerical experiments indicate that our approach is numerically stable even for ill-conditioned problems.

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Marc Van Barel, Georg Heinig, and Peter Kravanja "Solving Toeplitz least-squares problems via discrete polynomial least-squares approximation at roots of unity", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); https://doi.org/10.1117/12.406493

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