A total least squares method for Toeplitz systems of equations
The Newton method is used to solve the total least squares (TLS) problem for Toeplitz systems (a Toeplitz matrix has constant entries on each diagonal). TLS differs from the usual \(\text{LS} (Tf\approx g)\) in that both \(T\) and \(g\) are corrupted by errors. The Newton method requires the solution of a linear system and the authors present a preconditioned conjugate gradient method for this; either \(LDL^T\) factorization, or a circulant approximation, are suggested for the preconditioner. When Newton's method is coupled with a bisection scheme, it is shown that global convergence can be guaranteed. The paper concludes with some numerical tests comparing results of three variants of the basic scheme.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 1228555
scientific article