Fast algorithms for the regularization of banded Toeplitz least squares problems
James G. Nagy · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
An algorithm for computing solutions to ill-conditioned banded Toeplitz least squares problems by a rank revealing URV factorization is considered. The factorization is computed in O((beta) nlogn + (beta) n2), where (beta) is the bandwidth of the coefficient matrix. An approximate solution to ill-conditioned banded Toeplitz systems, in the presence of noise, is then obtained by truncating the factorization. Numerical results are provided that illustrate truncated URV can compute solutions comparable to the more expensive truncated singular value decomposition.