Subspace-by-subspace preconditioners for structured linear systems

We consider the iterative solution of symmetric positive-definite linear sy stems whose coefficient matrix may be expressed as the outer product of low -rank terms. We derive suitable preconditioners for such systems, and demon strate their effectiveness on a number of test examples. We also consider c ombining these methods with existing techniques to cope with the commonly-o ccuring case where the coefficient matrix is the linear sum of elements, so me of which are of very low rank. Copyright (C) 1999 John Wiley & Sons, Ltd .