The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. However, little is known about the behavior of this method when it is applied to the solution of nonsymmetric linear ill-posed problems with a right-hand side that is contaminated by errors. We show that when the associated error-free right-hand side lies ...

Flexible GMRES, introduced by Saad, is a generalization of the standard GMRES method for the solution of large linear systems of equations. It is based on the flexible Arnoldi process for reducing a large square matrix to a small matrix. We describe how the flexible Arnoldi process can be applied to implement one-parameter and multi-parameter Tikhonov regularization of linear discrete ill-posed...

The solution of nonsymmetric systems of linear equations continues to be a diicult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s>0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choic...

We construct, analyze and implement SSOR-like preconditioners for non-Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew-Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR-like iteration methods as well as the cor...

Standard multigrid algorithms have proven ineffective for the solution of discretizations of Helmholtz equations. In this work we modify the standard algorithm by adding GMRES iterations at coarse levels and as an outer iteration. We demonstrate the algorithm’s effectiveness through theoretical analysis of a model problem and experimental results. In particular, we show that the combined use of...

Direction of arrival estimation LFM signal is an essential task in radar, sonar, acoustics and biomedical. In this paper, a short time Fourier transform multi-step knowledge aided iterative generalized minimum residual (STFT-MS-KAI-GMRES) approach presented to amend the angle measurement signal. A three stage algorithm proposed. First, process initiated with formulating for carrier frequency ch...