4 papers
A Contour Method for Multiparameter Eigenvalue Problems
Emil Graf, Alex Townsend
Multiparameter eigenvalue problems arise in boundary value problems, stability analysis, and delay-differential equations. Despite their importance, existing methods either require…
Blow-up Parameter Landscapes for Polynomial Dynamical Systems
Emil Graf, Ioannis G. Kevrekidis, Alex Townsend
Finite-time blow-up is one of the ways in which a dynamical model can become singular, often signaling the breakdown of either the modeled physical system or the model itself. Dete…
A Hidden Variable Resultant Method for the Polynomial Multiparameter Eigenvalue Problem
Emil Graf, Alex Townsend
We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method…
Numerical Instability of Algebraic Rootfinding Methods
Emil Graf, Alex Townsend
We demonstrate that the most popular variants of all common algebraic multidimensional rootfinding algorithms are unstable by analyzing the conditioning of subproblems that are con…