Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems

Source abstract

Abstract We first derive some explicit bounds on the spectra of generalized non-symmetric singular or nonsingular saddle point matrices. Then we propose two new nonsingular preconditioners for solving generalized singular saddle point problems, and show that GMRES determines a solution without breakdown when applied to the resulting preconditioned systems with any initial guess. Furthermore, the detailed spectral properties of the preconditioned systems are analyzed. The nonsingular preconditioners are also applied to solve the singular finite element saddle point systems arising from the discretization of the Stokes problems to test their performance.