Some recent studies on Numerical Methods for Linear Systems

In this talk, two types of precondtioned iterative methods and SOR-like methods are proposed to solving saddle point problems. The upper bound of the condition number of the preconditioned systems are estimated. Semi-conjugate direction methods (SCD) are introduced as well. The properties of the SCD method are studied. The equivalence of the SCD methods and the LU decomposition is established. Some remedies for breakdown problem are presented. Some applications and open problems are mentioned for future research.