ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Abstract

Efficient solution of linear systems of equations is one of the central topics of numerical computation. Linear systems with complex coefficients arise from various physics and quantum chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve complex systems of linear equations. Theoretical analysis is given to highlight the basic features of our new algorithm. Four variants of our algorithm were also implemented and intensively tested on randomly generated full and sparse matrices and real-life problems. The results of numerical experiments reveal that our ABS-based algorithm is able to compute the solution with high accuracy. The performance of our algorithm was compared with a commercially available software, Matlab’s mldivide (\) algorithm. Our algorithm outperformed the Matlab algorithm in most cases in terms of computational accuracy. These results expand the practical usefulness of our algorithm.

Solution of the real and complex eigenvalue problems in the ABS class

“…This method will be compared with the MATLAB hess() function based on the work [6]. For the complex systems of linear equations of the ABS class see [5].…”