Preconditioned Iterative Methods for Solving Toeplitz-Plus-Hankel Systems

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-...

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

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

Generalized inversion of Toeplitz-plus-Hankel matrices

In many applications, e.g. digital signal processing, discrete inverse scattering, linear prediction etc., Toeplitz-plus-Hankel (T + H) matrices need to be inverted. (For further applications see [1] and references therein). Firstly the T +H matrix inversion problem has been solved in [2] where it was reduced to the inversion problem of the block Toeplitz matrix (the so-called mosaic matrix). T...