Stability of the Levinson Algorithm for Toeplitz-Like Systems
SIAM Journal on Matrix Analysis and Applications
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We present new fast algorithms for solving the Toeplitz and the Toeplitz-plus-Hankel least squares problems. These algorithms are based on a new fast algorithm for solving the Cauchy-like least squares problem. We perform an error analysis and provide conditions under which these algorithms are numerically stable. We also develop implementation techniques that significantly reduce the execution time. While no previous fast algorithm is known to be numerically stable for very ill conditioned problems, our numerical results indicate that these new algorithms are efficient and numerically stable for problems ranging from well conditioned to very ill conditioned to numerically singular.