Two efficient iteration methods for solving the absolute value equations

Two efficient iteration methods are proposed for solving the absolute value equation which are the accelerated generalized SOR-like (AGSOR-like) iteration method and the preconditioned generalized SOR-like (PGSOR-like) iteration method. We prove the convergence of the two proposed iterative methods after applying some qualification conditions to the parameters involved. We also discuss the optimal values of the parameters involved in the two methods. Also, some numerical experiments demonstrate the practicability, robustness and high efficiency of the two new methods. In addition, applying the optimal parameter values obtained from theoretical analysis to the PGSOR-like method, it can give solutions with high accuracy after a small number of iterations, demonstrating significant advantages.