A class of linear solvers built on the Biconjugate A-Orthonormalization Procedure for solving unsymmetric linear systems

TL;DR

This paper introduces a new family of efficient iterative solvers based on the Biconjugate A-Orthonormalization Procedure, which are fast, memory-efficient, and outperform existing methods for solving unsymmetric linear systems.

Contribution

The paper develops a novel class of linear solvers built on the Biconjugate A-Orthonormalization Procedure, demonstrating superior performance over traditional Arnoldi and biconjugate Lanczos methods.

Findings

Solvers are fast convergent and memory-efficient.

Numerical experiments show they outperform popular existing algorithms.

The methods are effective for both real and complex non-Hermitian systems.

Abstract

We present economical iterative algorithms built on the Biconjugate $A$-Orthonormalization Procedure for real unsymmetric and complex non-Hermitian systems. The principal characteristics of the developed solvers is that they are fast convergent and cheap in memory. We report on a large combination of numerical experiments to demonstrate that the proposed family of methods is highly competitive and often superior to other popular algorithms built upon the Arnoldi method and the biconjugate Lanczos procedures for unsymmetric linear sytems.