A parameterized block-splitting preconditioner for indefinite least squares problem

TL;DR

This paper introduces a new parameterized block-splitting preconditioner for indefinite least squares problems, enhancing GMRES convergence and analyzing spectral properties, with demonstrated numerical efficiency improvements.

Contribution

It proposes a novel parameterized block-splitting preconditioner specifically designed for indefinite least squares problems, including convergence analysis and spectral distribution insights.

Findings

The preconditioner accelerates GMRES convergence.

Optimal parameter selection improves performance.

Numerical results outperform existing preconditioners.

Abstract

We present a stationary iteration based upon a block splitting for a class of indefinite least squares problem. Convergence of the proposed method is investigated and optimal value of the involving parameter is used. The induced preconditioner is applied to accelerate the convergence of the GMRES method for solving the problem. We also analysed the eigenpair distribution of the preconditioned matrix. {We assess the efficiency of the proposed preconditioner by presenting results from a numerical comparison with several existing preconditioners.