Numerical Interative Methods For Solving The Linear Saddle Point Problems

With the development of science and technology, Calculation mathematics is becoming more and more important for large amount of calculation in other branch of mathematics and engineering, so it becomes a very important branch of mathematics. A comparatively important aspect of Calculation mathematics is to solve the large linear equations. For solving the large linear equations it has two main methods: iterative methods and direct solution methods. Until recently, direct solution methods were often preferred over iterative methods in real applications because of their robustness and predictable behavior. However, a number of efficient iterative solvers were discovered and the increased need for solving very large linear systems triggered a noticeable and rapid shift toward iterative techniques in many applications.In fact, solving the linear saddle point problems is solving the solving the large linear equations. So to solve it generally adopt iterative methods. Linear saddle point problems arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems and numerous solution techniques have been proposed for solving this type system. For solving this problem Guo-Feng Zhang established the generalized symmetric SOR method, This paper aims at doing the extension of the GSSOR method further and study the convergence of the GSSOR method in this situation. In chapter 4 and chapter 5 the GSSOR method was applied to solve the nonlinear symmetrical saddle point problem and singular linear saddle point problem.