Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian (PS) splitting, and then establish a class of positivedefinite and skew-Hermitian splitting (PSS) methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving the positive definite systems of linear equations. Theoretical analysis shows that the PSS method converges Subsidized by The Special Funds For Major State Basic Research Projects G1999032803. Research supported, in part, by DOE-FC02-01ER4177. Supported by National Natural Science Foundation of China.