Cao, Yang A block positive-semidefinite splitting preconditioner for generalized saddle point linear systems. (English) Zbl 1434.65087 J. Comput. Appl. Math. 374, Article ID 112787, 15 p. (2020). Summary: In this paper, we propose a new block positive-semidefinite splitting (BPS) preconditioner for a class of generalized saddle point linear systems. The new BPS preconditioner is based on two positive-semidefinite splittings of the generalized saddle point matrix, resulting in an unconditional convergent fixed-point iteration method. Theoretical results show that all eigenvalues of the BPS preconditioned matrix are clustered at only two points as the iteration parameter is close to zero. Two numerical examples arising from the mixed finite element discretization of the linearized Navier-Stokes equation and the meshfree discretization of the piezoelectric structure equation are used to illustrate the effectiveness of the new preconditioner. Cited in 8 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L15 Numerical solution of eigenvalue problems involving ordinary differential equations 65F08 Preconditioners for iterative methods 65F10 Iterative numerical methods for linear systems Keywords:generalized saddle point linear system; block positive-semidefinite splitting; preconditioning; convergence Software:Matlab; IFISS PDFBibTeX XMLCite \textit{Y. Cao}, J. Comput. Appl. Math. 374, Article ID 112787, 15 p. (2020; Zbl 1434.65087) Full Text: DOI References: [1] Bai, Z.-Z., Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks, J. Comput. Appl. Math., 237, 295-306 (2013) · Zbl 1252.15022 [2] Benzi, M.; Golub, G. H.; Liesen, J., Numerical solution of saddle point problems, Acta Numer., 14, 1-137 (2005) · Zbl 1115.65034 [3] Benzi, M.; Golub, G. H., A preconditioner for generalized saddle point problems, SIAM J. Matrix Anal. 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