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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-01-01324-2

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

Published electronically:
May 14, 2001

Article copyright:
© Copyright 2001
American Mathematical Society