Preconditioning techniques for nonsymmetric and indefinite linear systems

摘要

The standard preconditioning techniques for conjugate gradient methods often fail for matrices that are indefinite and/or strongly nonsymmetric. The most common alterative considered for these cases are either to use expensive direct solvers or to resort to one of many techniques based on the normal equations. This paper examines several such alternatives and compares them. In particular an incomplete LQ factorization is proposed and some of its implementation details are described. A number of experiments are reported to compare these methods.