Block triangular preconditioners for symmetric saddle-point problems

In this paper we study the spectral properties and the computational performance of a block triangular preconditioner for the solution of the general symmetric saddle-point problem. We provide estimates for the region containing both the nonreal and the real eigenvalues. Moreover, we show that an indefinite inner product can be employed to devise an efficient short-term recurrence Krylov subspace solver to be used with the analyzed preconditioner. Numerical experiments on a variety of application problems are also reported. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.