Quick Solving Method For A Type Of Nonsingular Linear Equation

Following the electronic computer invention and quick development,calculation of science has become the third method,paralled to analysis of theory and experiment of science in all kinds of nature science and engineering technique science. At the same time numerical calculation is a necessary link solving the linear sysetem of equations,which is a very important question in numerical calculation. On the other hand, in math and physical department many questions had been solved by one or a few large-scale and sparse matrixs of linear equation.So,how to solve the large linear equation is the core of large-scale science and engineering project compution.Many authors have studied it (see[1]-[11]).There are two methods to solve the linear system of equations.They are direct solving method and iterative method. If the step of the linear system question is not very high, direct solving method is better. With the rapid development of computer,the scale of the problem becomes larger and larger.Direct method has been substituted by iterative method and iterative method has become one kind of the important methods for solving large linear equations.At this time, the rule of the iteration becomes a important question and a core question(see [12]-[17]).Usually, we use the iterative method, which are Jacobi, Gauss-Seidel,SOR,AOR,SAOR,SSOR and so on.These iterative methods is a good way to solve the linear equations. However,these iterative methods will be very slow,when the spectral radius go to one.So, we are necessary to find a quick solving method of the linear equations.The followings are the construction and main contents of this paper:In chapter one,we explain that the iterative solving method has much superiority in solving the linear system of equations and introduces the development in preconditioned theroy in recent years.In chapter two, we prove some results concering the convergence of the Peaceman-Pachord iterative method, when A is nonsingular M-matrix for the coefficient matrix of the linear system Ax=b.The spectral radius can be very small.In chapter three, we provide a new solving method for a size of linear systems equation,which can make the calculation speed be fast.In chapter four,numerical examples mainly verfy the results.