New Krylov-Subspace Solvers for Hermitian Positive Definite Matrices with Indefinite Preconditioners

Incomplete LDL* factorizations sometimes produce an indenite preconditioner even when the input matrix is Hermitian positive denite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive denite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can be preconditioned using any non-singular Hermitian matrix as long as the original system is positive denite. These algorithms allow the use of incomplete-factorization preconditioners for Hermitian positive-denite systems, even when the preconditioner is indenite, and without resorting to a more expensive non-symmetric iterative Krylov-space solver.

By: Haim Avron; Anshul Gupta; Sivan Toledo

Published in: RC24698 in 2008


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to .