A posteriori error bounds for the block-Lanczos method for matrix function approximation
Numerical Analysis
2024-04-16 v4 Numerical Analysis
Abstract
We extend the error bounds from [SIMAX, Vol. 43, Iss. 2, pp. 787-811 (2022)] for the Lanczos method for matrix function approximation to the block algorithm. Numerical experiments suggest that our bounds are fairly robust to changing block size and have the potential for use as a practical stopping criteria. Further experiments work towards a better understanding of how certain hyperparameters should be chosen in order to maximize the quality of the error bounds, even in the previously studied block-size one case.
Cite
@article{arxiv.2211.15643,
title = {A posteriori error bounds for the block-Lanczos method for matrix function approximation},
author = {Qichen Xu and Tyler Chen},
journal= {arXiv preprint arXiv:2211.15643},
year = {2024}
}