A Preconditioned MINRES method for nonsymmetric Toeplitz matrices

Author: 

Pestana, J
Wathen, A

Publication Date: 

19 March 2015

Journal: 

SIAM Journal on Matrix Analysis and Applications

Last Updated: 

2020-09-30T03:31:11.953+01:00

Issue: 

1

Volume: 

36

DOI: 

10.1137/140974213

page: 

273-288

abstract: 

Circulant preconditioning for symmetric Toeplitz linear systems is well established; theoretical guarantees of fast convergence for the conjugate gradient method are descriptive of the convergence seen in computations. This has led to robust and highly efficient solvers based on use of the fast Fourier transform exactly as originally envisaged in [G. Strang, Stud. Appl. Math., 74 (1986), pp. 171--176]. For nonsymmetric systems, the lack of generally descriptive convergence theory for most iterative methods of Krylov type has provided a barrier to such a comprehensive guarantee, though several methods have been proposed and some analysis of performance with the normal equations is available. In this paper, by the simple device of reordering, we rigorously establish a circulant preconditioned short recurrence Krylov subspace iterative method of minimum residual type for nonsymmetric (and possibly highly nonnormal) Toeplitz systems. Convergence estimates similar to those in the symmetric case are established.

Symplectic id: 

516209

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article