Iterative methods for solving absolute value equations
Rashid Ali, Asad Ali, S. Iqbal · Journal of Mathematics and Computer Science · 2021
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.