Expanded systems and the ILU preconditioner for solving non-Hermitian linear systems Original Research Article

Various iterative and direct methods for solving linear systems of equations are known. The Hermitian linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. Hence the aim of this paper is to consider the methods derived from a Hermitian augmented system – also called a Hermitian expanded system – and make a comparison with the generalized minimal residual method (GMRES). Finally, we will show how to apply the ILU preconditioner to a Hermitian expanded system, which gives us an advantage over the convergence of the method studied in this paper.