Research On The Iteration Algorithms For Complex Symmetric Linear Systems Based On Three Accelerating Techniques

Complex symmetric linear systems arise widely in a variety of scientific and engineering applications,and the solution of complex symmetric linear systems has become one of the key issues in scientific and engineering computation.It is of great theoretical and practical significance to study the efficient methods for solving the numerical solutions of the complex symmetric linear systems.Based on the parameter accelerating technique,the minimum residual technique and the preconditioning technique,we mainly study and improve the iterative algorithms for solving the large sparse complex symmetric linear systems,and propose some new efficient and stable iterative algorithms in this dissertation.The full dissertation is divided into five parts.In the first part,the research background of the large sparse complex symmetric linear systems,the development history of the related iterative algorithms and the research status at home and abroad are introduced.In addition,we explain some symbols which are useful to our main theorems in this dissertation.In the second part,we primarily introduce the TDSS and the ITDSS iteration methods for solving the complex symmetric linear systems by applying the parameter accelerating technique to the DSS and the IDSS ones,respectively.Secondly,by some theoretical analyses and derivations,the convergence properties of the TDSS and the ITDSS iteration methods are obtained.Finally,the effectiveness of these two iteration methods are validated by some numerical experiments when compared with some existing ones.In the third part,we primarily construct the TMRTTSCSP and the SMRTTSCSP iteration methods for solving the complex symmetric linear systems by applying the minimum residual technique to the TTSCSP one.Secondly,by some theoretical derivations and investigates,the convergence conditions and the theoretical optimal parameters of the TMRTTSCSP and the SMRTTSCSP iteration methods are obtained.Finally,the effectiveness and stability of these two iteration methods are validated by some numerical experiments when compared with some existing ones.In the fourth part,we primarily develop the PMBP iteration method for solving the twoby-two block complex symmetric linear systems by applying the preconditioning technique to the MBP one.Secondly,the convergence conditions,the optimal parameters and the optimal convergence factor of the PMBP iteration method are obtained by some theoretical derivations and investigates.Finally,the feasibility and superiority of the PMBP method are validated by some numerical experiments when compared with some existing ones.In the fifth part,we summarize and prospect the full dissertation.