Volume 1, pp. 11-32, 1993.
BiCGstab(
Gerard L. G. Sleijpen and Diederik R. Fokkema
Abstract
For a number of linear systems of equations arising from realistic
problems, using the Bi-CGSTAB algorithm of van der Vorst [17]
to solve these
equations is very attractive. Unfortunately, for a large class of
equations, where, for instance, Bi-CG performs well, the convergence of
Bi-CGSTAB stagnates. This was observed specifically in case of discretized
advection dominated PDE's. The stagnation is due to the fact that for this
type of equations the matrix has almost pure imaginary eigenvalues.
With his BiCGStab2 algorithm Gutknecht [5] attempted to
avoid this stagnation.
Here, we generalize the Bi-CGSTAB algorithm further, and overcome some
shortcomings of BiCGStab2.
In some
sense, the new algorithm combines GMRES(
Full Text (PDF) [296 KB], BibTeX
Key words
Bi-conjugate gradients, non-symmetric linear systems, CGS, Bi-CGSTAB, iterative solvers, GMRES, Krylov subspace.
AMS subject classifications
65F10.
ETNA articles which cite this article
| Vol. 2 (1994), pp. 57-75 Rüdiger Weiss: Minimization properties and short recurrences for Krylov subspace methods |
| Vol. 2 (1994), pp. 76-91 Ke Chen: Efficient iterative solution of linear systems from discretizing singular integral equations |
| Vol. 7 (1998), pp. 75-89 Gerard L. G. Sleijpen, Henk A. van der Vorst, and Ellen Meijerink: Efficient expansion of subspaces in the Jacobi-Davidson method for standard and generalized eigenproblems |
| Vol. 36 (2009-2010), pp. 126-148 Martin H. Gutknecht: IDR explained |