The Iterative Methods To Two Kinds Of Linear Systems

This paper studies two important problems, which are the iterative methods for large and sparse saddle point problems and an iterative method based on gradient to solve matrix equations(A1XB1,A2XB2)=(C1,C2). The structure is as follows:Section One introduces the background, theoretical and practical value about large sparse saddle point problems and matrix equations, then we give the latest achievement from domestic and foreign.In Section Two, we construct three iterative methods to solve saddle point problems, analysis its convergence, and show its efficiency by numerical examples.In the third Section, we construct an iterative method based on gradient to solve matrix equations, study its convergence and give the optimal convergence factor, finally two numerical examples are used to show its efficiency.Section Four gives the conclusion of the paper and prediction to the problems mentioned above.