Journal
IMA JOURNAL OF NUMERICAL ANALYSIS
Volume 27, Issue 1, Pages 1-23Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imanum/drl017
Keywords
saddle-point problem; Hermitian and skew-Hermitian splitting; splitting iteration method; preconditioning
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We establish a class of accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems by making use of the Hermitian and skew-Hermitian splitting (HSS) iteration technique. These methods involve two iteration parameters whose special choices can recover the known preconditioned HSS iteration methods, as well as yield new ones. Theoretical analyses show that the new methods converge unconditionally to the unique solution of the saddle-point problem. Moreover, the optimal choices of the iteration parameters involved and the corresponding asymptotic convergence rates of the new methods are computed exactly. In addition, theoretical properties of the preconditioned Krylov subspace methods such as GMRES are investigated in detail when the AHSS iterations are employed as their preconditioners. Numerical experiments confirm the correctness of the theory and the effectiveness of the methods.
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