A note on spectrum analysis of augmentation block Schur complement preconditioners

Authors:
Zhi-Hao Cao
Affiliations:
School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, People's Republic of China 200433
Venue:
Numerical Algorithms
Year:
2012

Citing 3
Cited 1

Matrix analysis

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Abstract

In this note, as a generalization of the preconditioner presented by Greif et al. (SIAM J Matrix Anal Appl 27:779---792, 2006), we consider a set of augmentation block Schur complement preconditioners for solving saddle point systems whose coefficient matrices have singular (1,1) blocks. The spectral properties of the preconditioned matrices are analyzed and an optimal preconditioner is derived.