Subspace-by-subspace Preconditioners for Structured Linear Systems

Abstract

We consider the iterative solution of symmetric positive-definite linear systems whose coefficient matrix may be expressed as the outer product of low-rank terms. We derive suitable preconditioners for such systems, and demonstrate their effectiveness on a number of test examples. We also consider combining these methods with existing techniques to cope with the commonly-occuring case where the coefficient matrix is the linear sum of elements, some of which are of very low rank. Copyright © 1999 John Wiley & Sons, Ltd.