Iterative solution of sparse linear systems

Linear systems of equations are encountered frequently in many problems in science and engineering.In large systems representing complicated problems, it is vital to make use of the sparsity of the problem. In such systems, using iterative methods rather than direct methods may decrease the time necessary for solutions.This theses is a survey of techniques used to obtain the solution of large sparse linear systems with emphasis on preconditioning. Mainly, we compare the number of arithmetic operations necessary to solve sparse linear systems using Gaussian elimination before and after reordering the coefficient matrix by Cuthill-McKee algorithm to reduce bandwidth.