Studies Of The Convergence Of The Iterative Methods With Several New Preconditioners

Iterative method is the common method for solving the linear equations, but with the increasing scale of linear equations, it will appear that the convergence rate of the solution is very slow with the extensive calculation, when using basic iterative method to solve the problems. The preconditioning technology can solve these problems well, in this dissertation, the preconditioned GAOR iterative method, the preconditioned MAOR iterative method, the preconditioned GMTS iterative method and the preconditioned multisplitting LUSAOR iterative method are studied.In the first chapter, some background relevant to this dissertation is introduced.In the second chapter, some definitions and lemmas relevant to this dissertation are listed.In the third chapter, the fourth chapter and the fifth chapter, the iterative forms of the GAOR iterative method, MAOR iterative method and the GMTS iterative method with the new forms of preconditioner are presented. Moreover, the convergence is also studied. Finally, the conclusions of the theorems are verified by some numerical examples.In the sixth chapter, the related contents of the multisplitting LUSAOR iterative method and the preconditioned multisplitting LUSAOR iterative method are introduced, and a new preconditioner is presented. In addition, the convergence of the preconditioned multisplitting LUSAOR iterative method is disscused. Finally, a numerical example is given to verify the conclusions are right.