A geometric method for eigenvalue problems with low rank perturbations
Spectral Theory
2017-08-14 v2 Analysis of PDEs
Neurons and Cognition
Abstract
We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a well-understood operator, motivated by a number of problems of applied interest which take this form. We use the fact that the system is a low rank perturbation of a solved problem, together with a simple idea of classical differential geometry (the envelope of a family of curves) to completely analyze the spectrum. We use these techniques to analyze three problems of this form: a model of the oculomotor integrator due to Anastasio and Gad (2007), a continuum integrator model, and a nonlocal model of phase separation due to Rubinstein and Sternberg (1992).
Cite
@article{arxiv.1705.07360,
title = {A geometric method for eigenvalue problems with low rank perturbations},
author = {Thomas J. Anastasio and Andrea K. Barreiro and Jared C Bronski},
journal= {arXiv preprint arXiv:1705.07360},
year = {2017}
}