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Constraint preconditioning for indefinite linear systems.(English)Zbl 0960.65052

The problem of finding good preconditioners for the numerical solution of indefinite linear systems of equations is considered. Special emphasis is put on preconditioners that have a \(2\times 2\) block structure and their incorporate the (1,2) and (2,1) blocks of the original matrix. Results concerning the spectrum and form of the eigenvectors of the preconditioned matrix and its minimal polynomial are given. The consequence of these results are considered for a variety of Krylov subspace methods. Numerical experiments confirm the conclusions.

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices

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