Several Kinds Of Methods For Solving Nonsymmetric Saddle Point Problems

Saddle point problems arise from many scientific and engineering computations such as fluid dynamics,the finite element method for solving the Navier-Stokes equa-tion,constrained least squares problems,constrained optimization problems and so on.This paper discusses the nonsymmetric saddle point problem,It is mainly divid-ed into the standard nonsymmetric saddle point problem and the nonsymmetric gen-eralized saddle point problem,and they can be divided into singular nonsymmetric(generalized)saddle point problem and the non-singular nonsymmetric(generalized)saddle point problem.Since the above problems are large and squares,the iterative methods are effective for solving the storage space and decreasing the computation time,so it is very important to study of the effective iterative methods for saddle point problems.Recently,many researchers have proposed some effective methods,such as Uzawa methods,HSS methods and so on.In this paper,we mainly study the iterative methods for nonsymmetric saddle point problems and nonsymmetric generalized saddle point problems.First,we give a new Uzawa method for non-symmetric saddle point problems,and analysis the convergence.Secondly,we prove the modified shift-splitting(MSS)method for nonsymmetric generalized saddle point problems,and analysis the convergence and spectral analysis of the preconditioned matrix.Finally,we give the extended shift-splitting(ESS)method of nonsymmet-ric generalized saddle point problem,and analyze the convergence of this method in solving the nonsingular nonsymmetric generalized saddle point problem and the semiconvergence when solving singular nonsymmetric saddle point problem.