Transpose-Free Formulations of Lanczos-Type Methods for Nonsymmetric Linear Systems

Authors

Tony F. Chan, University of California - Los Angeles
Lisette G. de Pillis, Harvey Mudd CollegeFollow
Henk van der Vorst, University of Utrecht

Document Type

Article

Department

Mathematics (HMC)

Publication Date

5-1998

Abstract

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing A^T. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm.

Rights Information

© 1998 Kluwer Academic

DOI

10.1023/A:1011637511962

Recommended Citation

T.F. Chan, L.G. de Pillis, and H.A. van der Vorst "Transpose-Free Formulations of Lanczos-Type Methods for Nonsymmetric Linear Systems", Numerical Algorithms, Vol. 17, pp.51-66, 1998.