A Class Of Numerical Methods For Solving Complex Symmetric Linear Equations

It is meaningful to find an efficient method to solve complex symmetric linear systems problem based on the needs of various scientific calculations.This paper mainly proposes three iterative methods to solve complex symmetric linear systems,and verifies their effectiveness in the numerical experiments.The main research content is divided into the following four parts.Firstly,a PGAOR iterative method for solving complex symmetric linear systems is proposed.The sufficient condition of the iteration convergence is obtained by the convergence analysis.Secondly,a new accelerated generalized symmetric successive overrelaxation(AGSSOR)iterative method for solving complex symmetric linear systems is proposed.The AGSSOR iteration method is applied to the pretreatment system to obtain the corresponding PAGSSOR iteration method.Through the discussion of the iterative parameters,it is found that the selection of parameters within certain ranges can make thespectral radius of the PAGSSOR iterative matrix smaller than the spectral radius of the AGSSOR iterative matrix.Thirdly,a PSMSNS iterative method for solving complex symmetric linear systems is proposed.Through convergence analysis,the optimal parameters that minimize the upper bound of the iterative array radius is obtained.Fourthly,numerical experiments are carried out to verify the effectiveness of the proposed iterative methods and the PGAOR iteration method is compared with PAGSSOR iteration method.