A Class Of Preconditioners For Generalized Saddle Point Prob-lems

In this paper, the diference between the two matrices is minimizedby F-norm and the approximated matrix to the generalized saddle pointproblems similar matrix G is given. Then, the preconditioning matrix iscaculated by the theory of ST with the D we had. At the same time,relationship between the condition number of the preconditioning matrixG and D is proved by the theory of symmetric-position-definite matrix andST decomposition. The paper include four parts.In the first chapter, the application and classification of saddle pointproblems are introduced, and the development of preconditioning matrixare also introduced.In the second chapter, some research results of ST decomposition aredescribed.In the third chapter, a new preconditioner is presented.In the last chapter, a numerical example is presented, we can verifythat the condition number of the preconditioning matrix is less than theoriginal coefcient matrix. At the end of paper the conclusion are given.