Research On Generalized Constant Iteration Algorithm

The rapid progress of modern science and technology makes the calculation of some large-scale projects more and more huge, and how to solve a series of large sparse linear equations on the field of scientif-ic computing and numerical algebra research field is a very important research topic. Many engineering problems and the development of sci-entific research and research are related to large-scale computing, it can be said that in today's society, the efficiency of computing has affected the development of society. Such as the calculation of fluid mechanics,the collection and processing of oil seismic data, the prediction of nu-merical weather, the optimal design of the power system, and so on, the traditional direct calculation method has almost failed for large-scale numerical calculation. To deal with these problems, we must, establish an effective model, and finally return to the linear equations Ax = b on the numerical solution. In this paper, we study several generalized iter-ative algorithms, and realize the selection of some optimal parameters.The paper mainly has the following three parts.First, the unsymmetric SOR-like method (USSOR) is used to solve the least, squares problem and the optimal parameters are obtained. The GMRES algorithm is used to accelerate the preprocessing matrix.Secondly, modifing the generalized parameterized inexact Uzawa method(GPIU) to get a new method named MGPIU method. Using the MGPIU method to solve the singular saddle point problems, and the semi-convergence of the method is proved. By selecting the appro-priate parameters, numerical experiments are carried out to give the effectiveness of the method.Thirdly, Comparing the two kinds of generalized constant iteration,the iteration matrix is M(?)N and I- M(?) A. Based on the analysis of the spectrum of the iterative matrix and the coefficient matrix of the pre-treatment system, the generalization of some results of the generalized stationary iteration is realized.