Preconditioning and Iterative Methods for Complex Linear Systems

Zhong-Zhi Bai
Institute of Computational Mathematics and Scientific/Engineering Computing
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
Beijing, P.R.China


For a class of complex symmetric systems of linear equations, by modifying the Hermitian and skew-Hermitian splitting (HSS) iteration method and making use of the special structure of the coefficient matrix, we describe a class of matrix splitting iteration schemes, which is unconditionally convergent for any initial guess. In the talk, we also discuss real equivalent reformulations of these matrix splitting iteration schemes and apply them to solve and precondition the saddle-point linear systems, arising from the Galerkin finite-element discretizations of the distributed control problems.