Analysis Of The Convergence Of The Two Preconditioned Iterative Methods

On this day in the twenty-first Century, many practical problems cannot solvewithout the linear equations, the iterative method is the common method to solve thequestions. But using of iterative method to solve linear equations, the convergencespeed sometimes would be slow or even not convergent, which consume more time.In order to solve the above problems, it is need to improve the rate ofconvergence of the iterative methods. This article has researched the preconditionedGAOR iteration method and the preconditioned GMTS iteration method.In the first chapter and the second chapter, the relevant background and therelated basic knowledge are introduced.In the third chapter and the fourth chapter, firstly, introduces the generalizedaccelerated overrelaxation iterative method (GAOR iterative method), then severalkinds of new processing factors and the relevant content of the preconditionedGAOR iteration method are given, discusses the convergence of the preconditionedGAOR iteration method. Finally, the example is given to prove the conclusions.In the fifth chapter, the generalized mixed splitting iterative method (GMTSiterative method) and the preconditioned GMTS iterative method are introduced,then studies the comparison of the convergence between the preconditioned GMTSiterative method and GMTS iterative method, the theorems shows it is better to usethe preconditioned GMTS iterative method. Finally, the example is given to provethe conclusions.