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Liesen, Jörg; Ramme, Justus

Spectral properties of certain nonsymmetric saddle point matrices. (English) Zbl 07881194

ETNA, Electron. Trans. Numer. Anal. 60, 276-291 (2024).
Summary: We consider certain (real) nonsymmetric matrices in saddle point form, study their general Jordan normal forms, and prove new conditions so that these matrices are diagonalizable with a real spectrum. For matrices satisfying our conditions we show how to construct an inner product in which these matrices are selfadjoint. Our approach generalizes previously published results in this area, which require stronger assumptions on the given saddle point matrices and hence are less widely applicable.

MSC:

15A20 Diagonalization, Jordan forms
15A18 Eigenvalues, singular values, and eigenvectors
65F10 Iterative numerical methods for linear systems

Keywords:

saddle point problems; eigenvalues and eigenvectors; conjugate gradient iterations; Krylov subspace methods

Software:

IFISS
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Full Text: DOI Link

References:

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