A fast spectral divide-and-conquer method for banded matrices
Numerical Analysis
2018-01-22 v1 Numerical Analysis
Abstract
Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3): A1325-A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For this purpose, we combine our previous work on the fast computation of spectral projectors in the so called HODLR format, with a novel technique for extracting a basis for the range of such a HODLR matrix. The numerical experiments demonstrate that our algorithm exhibits quasilinear complexity and allows for conveniently dealing with large-scale matrices.
Cite
@article{arxiv.1801.04175,
title = {A fast spectral divide-and-conquer method for banded matrices},
author = {Ana Šušnjara and Daniel Kressner},
journal= {arXiv preprint arXiv:1801.04175},
year = {2018}
}
Comments
21 pages, 6 figures