Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation, 71 (238):
479--506 (May 2001)DOI: 10.1090/s0025-5718-01-01324-2
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.