| Following the electronic computer's invention and quick development, calculation of science has become the third method, paralleled to analysis of theory and experiment of science in all kinds of natural science and engineering technique science. At the same time calculation of numerical value is a necessary link solving the linear system of equations, which is a very important question in calculation of numerical value.There are two methods to solve the linear system of equations. They are direct solving method and iterative solving method. If the step of the linear system question is not very high, direct solving method is better; if coefficient matrix of the linear system question is not regular and large-sparse matrix (a lot of element is equal zero) , direct solving method does not settle the storage question. However, in many practical problem of the linear system question, the linear system of equations has some important characteristic especially in leaning differential equation method and limited element method. The first characteristic is large-scale and sparse matrix; the second is satisfactory with some conditions, for example, diagonal advantage, symmetry etc. Comparing with direct solving method, the iterative solving method has some obvious advantages. This thesis mainly deals with the iterative method to solve the linear system of equations and discuss how to accelerate the rate of convergence in the condition of precondition.Throughout the thesis, a linear system matrix is of the from Ax = b ,with A = (aij)n×n, x,b∈ Rn, x is an unknown vector, b is a known vector. The thesisproper contains from chapter one to chapter five, now give details:Chapter one explains that the iterative solving method has much superiority insolving the linear system of equations and introduces the development in preconditionedtheory in recent years.In chapter two, the writer provides the basic knowledge and the basic lemmarequired in this paper.
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