A two-step fixed-point iterative scheme for solving Generalized Absolute Value Matrix Equations

Abstract

This study introduces a numerical approach for solving the Generalized Absolute Value Matrix Equation. The motivation of this work lies in the fact that such equations arise in various applied mathematical and engineering problems, where the presence of the absolute value term makes the system strongly nonlinear and difficult to solve using standard linear algebra techniques. The elementwise absolute value introduces a nonlinearity, which makes standard linear solvers unsuitable. A tailored two-step fixed-point iteration is developed and tested on problems of varying sizes. Numerical experiments demonstrate that, with a suitable relaxation parameter, the method achieves reliable convergence, maintaining robustness and accuracy even for moderately sized problems.