Abstract
Among the iterative methods for solving large linear systems with a sparse (or, possibly, structured) nonsymmetric matrix, those that are based on the Lanczos process feature short recurrences for the generation of the Krylov space. This means low cost and low memory requirement. This review article introduces the reader not only to the basic forms of the Lanczos process and some of the related theory, but also describes in detail a number of solvers that are based on it, including those that are considered to be the most efficient ones. Possible breakdowns of the algorithms and ways to cure them by look-ahead are also discussed.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Numerical Analysis
Reference160 articles.
1. A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
2. Generalized conjugate gradient squared
3. Fokkema D. R. (1996 b), Subspace Methods for Linear, Nonlinear, and Eigen Problems, PhD thesis, Utrecht University.
4. Day D. M. , III (1993), Semi-duality in the two-sided Lanczos algorithm, PhD thesis, University of California at Berkeley.
Cited by
76 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献