A Class Of Convergence And Divergence Analysis USSOR Preconditioned Iterative Method

Many problems in mathematics,physics,hydrodynamics,engineering and eco-nomics are attributed to solving one or several the large-scale sparse linear alge-braic equations.It is well known,two methods are usually adopted to solve the linear system Ax=b.That is,the direct method and the iterative method.The direct solv-ing method is convenient for the linear system when the order is not very high. The accurate answer will be produced through several limited operations if there is no rounding errors.Iterative method is widely used to solving linear systems for its less storage space and uncomplicated procedure engineering,especially present-ing more superiorly in large-scale numerical computing.So iterative method becomes a very important method for solving the large-scale linear algebraic equations.The rule of the iterative whether good or not is usually described by convergence and convergence rate.Thus,in order to own practical value,an iterative method which has good convergence and faster convergence rate should be find. Under general cir-cumstances,speed of convergence of iterative methods are adopted by measuring its spectral radius of iterative matrices.To effectively solve linear systems as soon as possible,nonsingular preconditioner is quoted.The convergence rate of iterative method is accelerated by preconditioner.Generally speaking,convergence of iterative methods have a close relationship with the properties of coefficient matrix. With the difference of coefficient matrix,the research method is different.According to [l],two preconditioners are firstly pro-posed;then assumed the coefficient matrix as an irreducible nonsingular L-matrix,with the theory of matrix splitting and eigenvalue vector method,spectral radius of Un-symmetrical Successive Overrelaxation method between before and after precondi-tion are compared,comparison theorems of convergence and divergence is derived and proved.Finally,numerical examples are used to verify the results of the proposed theories.To a certain extent,the existing conclusions are extended and improved in this paper.