Rectangular eigenvalue problems
Numerical Analysis
2021-12-28 v1 Numerical Analysis
Abstract
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems. The method applies equally in the limit "m=infinity" of eigenvalue problems for quasimatrices. Numerical examples are presented as well as pointers to some related literature.
Cite
@article{arxiv.2112.13698,
title = {Rectangular eigenvalue problems},
author = {Behnam Hashemi and Yuji Nakatsukasa and Lloyd N. Trefethen},
journal= {arXiv preprint arXiv:2112.13698},
year = {2021}
}