Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. (English) Zbl 1079.65028

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, the authors introduce a new splitting, called positive-definite and skew-Hermitian splitting (PSS), and then establish a class of PSS methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS) method for iteratively solving positive-definite systems of linear equations.
The convergence of the PSS iteration method is proved, and a theoretical analysis shows that the PSS iteration method preserves all advantages of both HSS and NSS iteration methods. By specializing the PSS to block triangular (or triangular) and skew-Hermitian splittings (BTSS or TSS), the PSS method directly results in a class of BTSS or TSS iteration methods for solving systems of linear equations.
Numerical examples are implemented to show that in the sense of computational storage and CPU time, the TSS and BTSS iteration methods are much more practical and effective as iterations schemes than the HSS iteration method, and they are also much more practical and effective as preconditioners than the ILU factorization and the UGS iteration.


65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
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