Matías R. Bender
Inria Saclay – CMAP, École Polytechnique
A new symbolic-numeric method to solve the multiparameter eigenvalue problem
21 March 2024, 5pm
KU Leuven, Department of Electrical Engineering (ESAT)
Aula C (ELEC B91.300)
Abstract
A classical approach to solving polynomial systems is to linearize the problem and reduce it to an eigenvalue calculation. For this purpose, certain families of special matrices are used, e.g., Sylvester and Dixon matrices. Their size and structure determine how far these methods can go; therefore, it is essential to construct better matrices for the specific systems that arise in practice. In this talk, we focus on polynomial systems coming from the multiparameter eigenvalue problem and certain generalizations. Using the theory of resultants and Weyman complexes, we present new matrices of optimal size for solving these systems. This talk is based on joint work with Jean Charles Faugère, Angelos Mantzaflaris, and Elias Tsigaridas.
