Several Iterative Methods For Large Linear Equations

In many fields of the modern scientific computing, such as theanaysis of circuit system, computational fluid dynamics, nonlinear pro-gramming，etc. How to solve these problems is attribute to solve the largelinear equations. Therefore, how to solve the large linear equations (linearsystems) efficiently is very important. In this paper, we mainly researchseveral iterative methods to solve the linear systems, the results are di-vided to four parts.Firstly, by the research for singular and nonsingular non-Hermitianpositive semi-definite linear systems, we give the convergent prosperityof the P-regular splitting iterative methods, which generalize the knownresults.Secondly, we present a generalized preconditioned Hermitian andskew-Hermitian splitting method (GPHSS) with two parameters, which isused to solve singular saddle point problems, we give the conditions of the semiconvergent of this method, and analyze the spectral property ofthe corresponding preconditioned matrix. Finally, numerical experimentsare given to illustrate the efficiency of GPHSS method with appropriateparameters both as a solver and as a preconditioner.Thirdly, we study the generalized inexact parameterized Uzawamethods for solving singular saddle point problems with nonsymmetric(1,1) blocks. Then, we give the convergent conditions of this method.Fourth, we compare the convergence performance of different itera-tive methods for solving singular and nonsingular linear systems throughseveral numerical experiments.