Iterative Algorithm For Solving Complex Symmetric Linear Systems Based On Acceleration Technique

Complex symmetric linear systems are widely derived from the fields of science and engineering computation.In solid mechanics,scientific computation,dynamics,engineering computation,nonlinear programming and other fields,it is necessary to solve complex symmetric linear systems.Therefore,it is of great theoretical significance and practical application value to study the effective algorithms of complex symmetric linear systems.This thesis mainly studies the new iterative method by using matrix splitting for solving large sparse complex symmetric linear systems.The full thesis is divided into five parts.In the first part,we mainly introduce the definition of iterative method,the development history of iterative method and the research status at home and abroad.We introduce some symbols used in this thesis.In the second part,an extrapolated modified quasi-Hermitian and skew-Hermitian splitting(EMHSS)iterative method is established by using extrapolation acceleration technique for modified Hermitian and skew-Hermitian splitting(MHSS)iterative method,and its convergence performance is analyzed.Finally,the practical examples are used to illustrate the effectiveness of the EMHSS iterative method.In the third part,based on the EMHSS iteration method proposed in the second part,we use the preprocessing acceleration technology to proposed a preprocessing extrapolated MHSS(PEMHSS)iteration method.In theory,we give the upper bound of the spectral radius of the PEMHSS iteration matrix,and discuss the conditions that the upper bound is less than 1.Finally,numerical experiments also show the effectiveness of the PEMHSS iterative method.In the fourth part,a symmetric positive definite matrix V is introduced to apply the acceleration technique to the modified quasi-Hermitian and skew-Hermitian splitting(MQHSS)iterative method to obtain a preprocessed MQHSS(PMQHSS)iterative method.The convergence properties of the PMQHSS iterative method are analyzed,and the convergence conditions when V = T are discussed.The properties of the PMQHSS iterative method when used as a preprocessor are also given.The practical numerical experiments show that the PMQHSS iterative method has better numerical results.In the fifth part,we use the lopsided acceleration technique to obtain a lopsided PMQHSS(LPMQHSS)iteration method for the PMQHSS iteration method proposed in the fourth part In addition,the first step of the PMQHSS iterative method uses the lopsided technology and takes V = T,and the second step of the PMHSS iterative method also uses the lopsided technology.Combines the two steps to obtain the double lopsided PMQHSS(DLPMQHSS)iterative method.We discuss the convergence conditions of the LPMQHSS iterative method and DLPMQHSS iterative method,and give the convergence properties of the LPMQHSS iterative method when V = T.Finally,numerical experiments show the effectiveness and superiority of our method.