A Look-ahead Variant of the Lanczos Algorithm and Its Application to the Quasi-minimal Residual Method for Non-hermitian Linear Systems

@inproceedings{Nachtigal1991ALV,
  title={A Look-ahead Variant of the Lanczos Algorithm and Its Application to the Quasi-minimal Residual Method for Non-hermitian Linear Systems},
  author={Maurice Nachtigal and Alar Toomre and Sigurdur Helgason and Roland Freund and Martin H. Gutknecht},
  year={1991}
}
The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition , the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. In this thesis, we present two… CONTINUE READING