# 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

### Abstract:

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.