Solving singular systems by hybrid of Electromagnetism Meta-Heuristic method and the GMRES method

GMRES is a popular iterative method for the solution of large linear systems of equation Ax=b with a sparse nonsingular matrix. When A is singular or nearly so, i.e., ill conditioned, GMRES may breakdown before an acceptable approximate solution has been determined. This paper presents a hybrid of GMRES method and Electromagnetism Meta-Heuristic method to overcome the breakdown. Both consistent and inconsistent systems are considered. Numerical examples are used to show the good numerical properties