Exploring two new iterative methods for solving absolute value equations

Numerous challenges arising in diverse fields such as scientific computing, operations research, management science, and engineering can be addressed by solving absolute value equations (AVEs). This paper introduces two innovative methods called the fixed point method and the modified generalized Gauss-Seidel method for solving AVEs. We delve into the convergence analysis of these methods under appropriate assumptions. Furthermore, we conduct three sets of numerical experiments to assess the practical feasibility of our proposed methods. The results obtained are encouraging and pave the way for further study in this domain.