Geodesic
Preconditioning of GMRES by the skew-Hermitian iterations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 3, pp. 267-279

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A class of preconditioners for solving non-Hermitian positive definite systems of linear algebraic equations is proposed and investigated. It is based on the Hermitian and skew-Hermitian splitting of the initial matrix. The generalization for saddle point systems which have semidefinite or singular $(1,1)$ blocks is given. Our approach is based on an augmented Lagrangian formulation. It is shown that such preconditioners are effective for the iterative solution of systems of linear algebraic equations by the GMRES. 
@article{SJVM_2016_19_3_a2,
     author = {L. A. Krukier and T. S. Martynova},
     title = {Preconditioning of {GMRES} by the {skew-Hermitian} iterations},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {267--279},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_3_a2/}
}
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L. A. Krukier; T. S. Martynova. Preconditioning of GMRES by the skew-Hermitian iterations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 3, pp. 267-279. http://geodesic.mathdoc.fr/item/SJVM_2016_19_3_a2/