The generalized double shift-splitting preconditioner for nonsymmetric generalized saddle point problems from the steady Navier–Stokes equations
 作者： Hong-Tao Fan,  Xin-Yun Zhu,  Bing Zheng 作者单位： 1School of Mathematics and Statistics, Lanzhou University2Institute of Applied Mathematics, College of Science, Northwest A&F University3Department of Mathematics, University of Texas of the Permian Basin 刊名： Computational and Applied Mathematics, 2018, Vol.37 (3), pp.3256-3266 来源数据库： Springer Journal DOI： 10.1007/s40314-017-0510-5 关键词： Nonsymmetric generalized saddle point problem;  Generalized double shift-splitting;  Krylov subspace method;  Convergence; 英文摘要： Abstract(#br)In this paper, a generalized double shift-splitting (GDSS) preconditioner induced by a new matrix splitting method is proposed and implemented for nonsymmetric generalized saddle point problems having a nonsymmetric positive definite (1,1)-block and a positive definite (2,2)-block. Detailed theoretical analysis of the iteration matrix is provided to show the GDSS method, which corresponds to the GDSS preconditioner, is unconditionally convergent. Additionally, a deteriorated GDSS (DGDSS) method is proposed. It is shown that, with suitable choice of parameter matrix, the DGDSS preconditioned matrix has an eigenvalue at 1 with multiplicity n , and the other m eigenvalues are of the form $$1-\lambda$$ 1 - λ with $$|\lambda |<1$$ | λ | < 1 , independently of the Schur complement... matrix related. Finally, numerical experiments arising from a model Navier–Stokes problem are provided to validate and illustrate the effectiveness of the proposed preconditioner, with which a faster convergence for Krylov subspace iteration methods can be achieved.