The Iterative Algorithms For Singular Linear Systems

The present paper is concerned with the theoretical analysis and numerical algorithms for some classes of singular linear equations.As we all know not like with nonsingular linear equations,singular linear equations is more difficult to solve. In this paper,the consistant singular linear equations is studied. There are four chapters in all.In the first part the paper mainly introduces the scientific significance of singular linear equations and introduces some basic theoretical knowledge on which iterative solving method for solving singular linear equations is based.In the second part the paper mainly introduces double splitting iterations for positive semidefinite singular linear systems. some convergence results for double splitting iterations for solving positive semidefinite singular linear systems are presented. Moreover, the convergence of double splitting methods for generalized saddle point systems is studied, and a convergence condition for double splitting methods applied to this type of linear systems is given. In the third part the new alternating-direction iterative method is proposed based on matrix splittings for solving a class of saddle point problems. In addition numerical examples shows that the new alternating-direction iterative method has superiority in solving the class of saddle point problems.In the fourth part preconditioned QMR iterations for solving singular linear systems are presented. What is more the method of constructing preconditioners is generalized.A algorithm is presented to find a largest linear independent submatrix of coefficient matrix.