English

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 AXXB=FAX-XB=F, where FF 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}
}