The Study Of Iterative Methods And Preconditioning For Complex Symmetric Linear Equations

Large sparse complex linear systems widely arise in many scientific computing and engineering applications,so it is of great significance to find efficient ways to solve such problems.This paper mainly studies the iterative methods and preconditioning for complex symmetric linear systems.The main content of the research is divided into three parts.Firstly,the CRI iterative method for complex symmetric linear systems is discussed.A variant iterative method is further proposed,and the proof of convergence and optimal convergence factor is given.In theory,the variant of the CRI iterative method is compared with the CRI iterative method and the GPMHSS iterative method,respectively.Numerical experiments verify the effectiveness of the variant of the CRI iteration method.Secondly,based on the successive over-relaxation(SOR)iterative technique,the CRI-SOR iterative method for complex symmetric linear systems is proposed.The convergence properties of CRI-SOR iterative method are analyzed,and the calculation method and practical selection method of its optimal parameter are given.Numerical experiments verify that CRI-SOR iterative method can effectively improve the efficiency of the CRI iterative method for linear systems.Thirdly,the PSPHSS iterative method is studied.The convergence property of the coefficient matrix condition weakening in the linear system is analyzed.When preconditioning matrix V ?W T,the convergence properties of the PSPHSS iterative method and the optimal parameter of the minimum convergence radius are analyzed.Numerical experiments show the effectiveness of the preconditioning matrix.