Preconditioned Gauss-Seidel Iterative Method for Linear Systems

The large scale sparse linear systems often appear in a wide variety of areas of mathematics, physical, fluid dynamics and economics science. So, solving efficiently these systems aroused many authors, interests. The iterative method which can take full advantage of the sparse matrix, thereby saving memory cell, so it is a more practical way to solve large sparse linear algebraic equations. The rule whether the iterative is good is usually described by convergence and convergence rate, thus, we should find an iterative method which has good convergence and fast convergence rate, this owns practical value. In order to solve linear system faster and better, we accelerate the convergence rate of iterative method. For solving the linear system Ax = b, different preconditioned AOR methods have been proposed by many authors. In this paper, we will give comparison of spectral radius between preconditioned Gauss-Seidel iterative methods with basic Gauss-Seidel method and basic AOR with a new preconditioner. Numerical example is also given to illustrate our results.