Yuji Nakatsukasa
Oxford University, UK
(Multivariate) rootfinding via eigenvalues
28 November 2023, 5pm
KU Leuven, Department of Electrical Engineering (ESAT)
Aula L (ELEC 00.24)
streaming link: https://eu.bbcollab.com/guest/b68853a66942432fac03ae2804e75e1f
Abstract
A powerful idea for solving nonlinear (univariate or multivariate) rootfinding problems is to approximate the functions with simple ones such as polynomials or rational functions, and find the roots of the approximants.
I will discuss the algorithm behind the roots command for Chebfun2 objects that find the common roots of two bivariate functions. The algorithm uses the Bezout resultant, which turns the rootfinding problem into eigenvalue problems. We introduce techniques to improve the speed and conditioning of the eigenvalue problems. Time permitting, I will discuss finding roots of (univariate) rational functions given in various forms, again using eigenvalues.
Based on joint work with Vanni Noferini, Maria Quintana Ponce, Alex Townsend, and Nick Trefethen.
