The PGLPSS And GUSOR Iterative Methods With Their Convergence Analyses For Solving Saddle Point Problems

In the fields of engineering and scientific computing, we often encounter a class of saddle point problems to be solved, such as constrained optimization, computational fluid dynamics, weighted least-squares problems, mixed finite element methods for solving elliptic partial differential equations and Stokes problems, image processing and so on. How to solve these problems fast and efficiently becomes more and more significant.In this thesis for solving large sparse linear systems, the PGLPSS and GUSOR iterative methods are proposed and the convergence analyses are given in the case that the coefficient matrix is nonsingular and singular respectively. Meanwhile some sufficient conditions under which is convergent when some proper conditions being satisfied shall be presented. Finally we verify the efficiency and feasibility of the two iterative methods of PGLPSS and GUSOR in solving specific problems with numerical examples.