On Generalized Parameterized Inexact Methods And Its Preconditioning For Saddle Point Problems

Saddle point problems arises in many scientific computations and engineering ap-plications, such as mixed finite element methods for solving elliptic partial differential equations,constraint optimization,least squares problem,fluid dynamics,elasticity and so on.So it is of great interest to develop fast and efficient methods.In paper [43],a parameterized inexact inexact iterative methods for solving symmet-ric saddle point problems with the (2,2)-block being zero was considered.In this paper, we extend it to the large sparse nonsymmetric generalized saddle point problems case by allowing the(1,2)-block to be not equal to the (2,1)-block.We proved that the iteration method is convergent under certain conditions,the spectral radius and distribution of the preconditioned matrix ware discussed.With different of the parameter matrices in the matrix splitting,we get several algorithms for solving the nonsymmetric generalized sad-dle point problem. Numerical experiments are used to show that our methods are feasible.