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Mathematics of Computation

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Analysis of iterative methods for saddle point problems: a unified approach

Author: Walter Zulehner
Journal: Math. Comp. 71 (2002), 479-505
MSC (2000): Primary 65N22, 65F10
Published electronically: May 14, 2001
MathSciNet review: 1885611
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In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems. The obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature. A few numerical tests are given which confirm the sharpness of the estimates.

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Additional Information

Walter Zulehner
Affiliation: Institute of Analysis and Computational Mathematics, Johannes Kepler University, A-4040 Linz, Austria

Keywords: Indefinite systems, iterative methods, preconditioners, saddle point problems, Uzawa algorithm
Received by editor(s): March 3, 1998
Received by editor(s) in revised form: February 11, 1999, and May 30, 2000
Published electronically: May 14, 2001
Article copyright: © Copyright 2001 American Mathematical Society