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ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis, pp. 276-291, 2024/05/14
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.
Keywords: saddle point problems, eigenvalues and eigenvectors, conjugate gradient iterations, Krylov subspace methods