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Zbl 1114.65034
Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong
Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. (English)
[J] Math. Comput. 76, No. 257, 287-298 (2007). ISSN 0025-5718; ISSN 1088-6842/e

The authors give a necessary and sufficient condition for an arbitrary non-Hermitian positive semidefinite linear system so that the preconditioned Hermitian and skew-Hermitian splitting (PHSS) iteration method leads to an unconditionally convergent iteration sequence. This result is further specialized to block tridiagonal linear systems to obtain unconditional convergence conditions for the corresponding block PHSS iteration method.
[Liu Xinguo (Qingdao)]

MSC 2000:: *65F10 Iterative methods for linear systems
65F35 Matrix norms, etc. (numerical linear algebra)
65F50 Sparse matrices

Keywords: non-Hermitian matrix; positive semidefinite matrix; Hermitian and skew-Hermitian splitting; splitting iteration method; convergence; preconditioning; block tridiagonal linear systems

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