Iterative methods for solving absolute value equations

Abstract

We suggest and analyze some iterative methods called Jacobi, Gauss--Seidel, SOR (successive over-relaxation), and modified Picard methods for solving absolute value equations \( Ax-| x | = b \), where \( A \) is an \(M\)-matrix, \(b \in R^{n}\) is a real vector, and \(x \in R^{n}\) is unknown. Furthermore, we discuss the convergence of the suggested methods under suitable assumptions and represent their performance through our numerical results. Results are very encouraging and may stimulate further research in this direction.

Topics & Concepts