A parameterized splitting preconditioner for generalized saddle point problems

By using sherman-morrison-woodbury formula,we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. by analyzing the eigenvalues of the preconditioned matrix,we find that when α is big enough,it has an eigenvalue at 1 with multiplicity at least n,and the remaining eigenvalues are all located in a unit circle centered at 1. particularly,when the preconditioner is used in general saddle point problems,it guarantees eigenvalue at 1 with the same multiplicity,and the remaining eigenvalues will tend to 1 as the parameter α → 0. consequently,this can lead to a good convergence when some gmres iterative methods are used in krylov subspace. numerical results of stokes problems and oseen problems are presented to illustrate the behavior of the preconditioner. © 2013 wei-hua luo and ting-zhu huang.