The Study Of Iterative Methods For Large Sparse Linear Systems

This thesis mainly studies several classes of iterative methods for large sparse linear systems of equations. For the general linear algebraic equations, the con-vergence properties of several classes of iterative algorithms are given, and the necessary and sufficient conditions for the convergence of the splitting iterative algorithm are given. The estimation and optimization of the compression factor of several kinds of iterative methods are also discussed. Finally, the feasibility and effectiveness of the new method are verified by numerical experiments. It is consisted of five chapters.In Chapter 2, base on the MSNS methods, we will present a generalized MSNS method(GMSNS) for solving a class of complex symmetric linear systems.The new method GMSNS is actually a two-parameter two-step iterative method, which can optimize iterative process. The sequence of ierative produced by the generalized GMSNS mehtod is proved to be convergence to the unique solution of the complex symmetric linear system, respectively.Lastly,numercal experiments on a few model problems are used to illustrate the efficiency of the GMSNS method.In Chapter 3, considering the class of complex symmetric linear systems (W+ iT)= b, with W ∈Rn×n and T ∈ Rn×n being real symmetric indefinite matrix and real symmetric positive definite matrix, we proposed the GSHNS iteration mehtod based on the SHNS method. We show that GSHNS method is convergent when W is a real nonsingular symmetric matrix and T is a real symmetric positive definite matrix if parameters a and b meet cettain conditions. Lastly, numercal experiments on a few model problems are used to illustrate the efficiency of the GSHNS method.In Chapter 4, The DGPMHSS iteration method is used to accelerate the successive over relaxation, and we get the accelerated DGPMHSS (ADGPMHSS) iteration method, and the convergence theory of the algorithm is established.In Chapter 5, we summarize the full thesis and pointed out the further re-search work.