Subspace-by-subspace preconditioners for structured linear systems

We consider the iterative solution of symmetric positive-de nite linear systems whose coe cient matrix may be expressed as the outer-product of low-rank terms. We derive suitable preconditioners for such systems, and demonstrate their e ectiveness on a number of test examples. We also consider combining these methods with existing techniques to cope with the commonly-occuring case where the coe cient matrix is the linear sum of elements, some of which are of very low rank. 1 ENSEEIHT-IRIT, 2 rue Camichel, 31071 Toulouse CEDEX, France, EU Email : [email protected] and [email protected] 2 Department for Computation and Information, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, EU Email : [email protected] 3 Current reports available by anonymous ftp from joyous-gard.cc.rl.ac.uk (internet 130.246.9.91) in the directory \pub/reports". Department for Computation and Information Atlas Centre Rutherford Appleton Laboratory Oxon OX11 0QX January 20, 1998.