Structure Preserving Restarts of the Non-Symmetric Lanczos Algorithm via the Implicitly shifted LR algorithm
Computational Physics
2024-07-10 v1
Abstract
The implicitly shifted QR iteration is used as a restart procedure for the Arnoldi method for the calculation of a few dominant eigenvalues of a large matrix. We show that the underlying idea of implicit polynomial filtering can be utilized in much the same manner via the implicitly shifted LR iteration to create a restart procedure for the non-symmetric Lanczos algorithm for eigenvalue computations, which preserves the tri-diagonal structure of the reduced matrix.
Cite
@article{arxiv.2407.06561,
title = {Structure Preserving Restarts of the Non-Symmetric Lanczos Algorithm via the Implicitly shifted LR algorithm},
author = {Prabal S. Negi and Cristobal Arratia},
journal= {arXiv preprint arXiv:2407.06561},
year = {2024}
}