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In this paper, efficient direct and iterative methods are described for solving a large random sparse non-symmetric linear system. Such systems of linear equations of huge order arise in several applications such as physics, mechanics, signal processing and other applications of real life problems. For this reason, we try to develop direct and iterative methods for solving such systems of linear equations. The suggested direct method is based on the sparse LU-decomposition method (DSLU). The developed iterative methods include a Semi-iterative Method (SM), a Splitting-based Iterative Method (SIM) and a preconditioned GMRES method. We consider two types of preconditioners based on Incomplete LU-decomposition (ILU). We test and compare the numerical implementations of these methods on four numerical examples to demonstrate their efficiency. Results show that the proposed ILU preconditioners in GMRES reduce largely number of iterations and give very accurate solutions.

GMRES , Preconditioner ILU , Sparse system , Direct method

2008

مجله جامعه تشرين: العلوم الاساسيه

مجله جامعه تشرين: العلوم الاساسيه