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.
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