On the eigenvalues of a class of saddle point matrices |
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Authors: | Michele Benzi Valeria Simoncini |
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Institution: | (1) Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322, USA;(2) Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40127 Bologna, Italy;(3) CIRSA, Ravenna and IMATI-CNR, Pavia, Italy |
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Abstract: | We study spectral properties of a class of block 2 × 2 matrices that arise in the solution of saddle point problems. These
matrices are obtained by a sign change in the second block equation of the symmetric saddle point linear system. We give conditions
for having a (positive) real spectrum and for ensuring diagonalizability of the matrix. In particular, we show that these
properties hold for the discrete Stokes operator, and we discuss the implications of our characterization for augmented Lagrangian
formulations, for Krylov subspace solvers and for certain types of preconditioners.
The work of this author was supported in part by the National Science Foundation grant DMS-0207599
Revision dated 5 December 2005. |
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Keywords: | Primary 65F10 65N22 65F50 Secondary 76D07 |
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