## A generalized preconditioned HSS method for non-Hermitian positive definite linear systems.(English)Zbl 1198.65065

The paper presents a generalized preconditioned HSS (Hermitian and skew-Hermitian) spliting method for a large sparse non-Hermitian positive definite linear system.
The first section concerns iterative methods called HSS and preconditioned HSS(PHSS)methods based on the Hermitian/skew-Hermitian spliting, presenting also the algorithm of the new generalized preconditioned HSS method (or simply GPHSS method).
The second section focuses on the study of the convergence rate of the GPHSS iteration. This new two-parameter two-step iterative method can be generalized to the two-step splitting iterative framework. Also, for the upper bound of the spectral radius of the iteration matrix, the optimal parameters for the GPHSS method are provided.
In the third section the authors introduce an efficient preconditioner based on the incremental unknowns method. The efficiency of the GPHSS method is numerically tested. A comparison with the HSS and PHSS methods shows that the new method is more efficient.
In the last section, a concluding remark is given.

### MSC:

 65F10 Iterative numerical methods for linear systems 65F08 Preconditioners for iterative methods
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### References:

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