Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

Preconditioned Iterative Methods for Weighted Toeplitz Least Squares Problems

We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algori...

Preconditioned Iterative Methods for Weighted Toeplitz Least Square Problems

Preconditioned Iterative Methods for Solving Linear Least Squares Problems

New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...

Fast Iterative Methods for Solving Toeplitz-plus-hankel Least Squares Problems∗

In this paper, we consider the impulse responses of the linear-phase filter whose characteristics are determined on the basis of an observed time series, not on a prior specification. The impulse responses can be found by solving a least squares problem min ‖d − (X1 + X2)w‖2 by the fast Fourier transform (FFT) based preconditioned conjugate gradient method, for (M +2n−1)by-n real Toeplitz-plus-...

Comparison Results on Preconditioned GAOR Methods for Weighted Linear Least Squares Problems

We present preconditioned generalized accelerated overrelaxation methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give a numerica...