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Analysis of iterative methods for saddle point problems: a unified approach
Author(s):
Walter
Zulehner.
Journal:
Math. Comp.
71
(2002),
479-505.
MSC (2000):
Primary 65N22, 65F10
Posted:
May 14, 2001
MathSciNet review:
1885611
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Abstract:
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
Email:
zulehner@numa.uni-linz.ac.at
DOI:
10.1090/S0025-5718-01-01324-2
PII:
S 0025-5718(01)01324-2
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
Posted:
May 14, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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