On the singular values of matrices with high displacement rank
Numerical Analysis
2018-01-12 v2
Abstract
We introduce a new ADI-based low rank solver for , where has rapidly decaying singular values. Our approach results in both theoretical and practical gains, including (1) the derivation of new bounds on singular values for classes of matrices with high displacement rank, (2) a practical algorithm for solving certain Lyapunov and Sylvester matrix equations with high rank right-hand sides, and (3) a collection of low rank Poisson solvers that achieve spectral accuracy and optimal computational complexity.
Keywords
Cite
@article{arxiv.1712.05864,
title = {On the singular values of matrices with high displacement rank},
author = {Alex Townsend and Heather Wilber},
journal= {arXiv preprint arXiv:1712.05864},
year = {2018}
}