On spectral clustering of HSS preconditioner for generalized saddle-point matrices

Abstract For the nonsingular generalized saddle-point matrix of a Hermitian positive definite or semidefinite leading block, we rigorously analyze clustering property for the eigenvalues of the corresponding preconditioned matrix with respect to the Hermitian and skew-Hermitian splitting preconditioner. The result shows that these eigenvalues are clustered around 0 + , 2 − , and a few points located on the unit circle centered at 1, as the iteration parameter is close to 0.

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