TABLE OF CONTENTS In the last few years we have studied preconditioning techniques based on sparse approximate inverses and have found them to be quite effective.
B. Carpentieri , et al. SIAM Journal on Scientific Computing, Vol. 25 (2003)
The objective is to remove the smallest eigenvalues of A which are known to slow down the convergence of GMRES.
Jocelyne Erhel , et al. Journal of Computational and Applied Mathematics, Vol. 69 (1996)
The most successful preconditioning methods in terms of reducing the number of iterations, such as the incomplete LU decomposition or symmetric successive relaxation (SSOR), are notoriously difficult to implement in a parallel architecture, especially for unstructured matrices.
Marcus J. Grote and Thomas Huckle . SIAM Journal on Scientific Computing, Vol. 18 (1997)
This chapter will discuss the construction of Inverse Type preconditioners (or approximate inverse type) i.e. for equation (1.2)
and other types as shown on Page 3. Our first concern will be a theoretical one on characterizing A ?1. It turns out that answering this concern reveals most underlying ideas of inverse type preconditioners. We shall present the following.
Section 5.1 How to characterize A?1 in terms of A
Section 5.2 Banded preconditioner
Section 5.3 Polynomial pk(A) preconditioners
Section 5.4 General and adaptive SPAI preconditioners
Section 5.5 AINV type preconditioner
Section 5.6 Multi-stage preconditioners
Section 5.7 The dual tolerance self-preconditioning method
Section 5.8 Mesh near neighbour preconditioners
Section 5.9 Numerical experiments
Section 5.10 Discussion of software and Mfiles
