Preconditioning linear systems via matrix function evaluation

TL;DR

This paper introduces a new preconditioned iterative method using matrix function evaluation, specifically designed for solving ill-posed problems and integrated with Tikhonov regularization, demonstrated through numerical experiments.

Contribution

The paper presents a novel preconditioning approach based on matrix function evaluation and extends it to Tikhonov regularization for improved solution of ill-posed problems.

Findings

Effective in solving integral equations

Applicable to image restoration tasks

Enhanced convergence with the proposed method

Abstract

For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method is also extended to work in connection with Tikhonov regularization. Numerical experiments arising from the solution of integral equations and image restoration are presented.