Bor Plestenjak
University of Ljubljana, Slovenia
Numerical methods for rectangular multiparameter eigenvalue problems
1 December 2023, 13h30-14h15
KU Leuven, Department of Electrical Engineering (ESAT)
ELEC B91.100
streaming link: https://eu.bbcollab.com/guest/4d2fa1a98fe8465094230c575de8b5a3
Abstract
Standard (square) multiparameter eigenvalue problems (MEPs) are systems of k linear k-parameter square matrix pencils, where we are looking for the k-tuples of parameters for which all k pencils are singular. Recently, a new form of MEPs has emerged: a rectangular MEP (RMEP) with only one multivariate rectangular matrix pencil, where we are looking for combinations of the parameters for which the rank of the pencil is not full. Applications include finding the optimal least squares autoregressive moving average (ARMA) model and the optimal least squares realization of autonomous linear time-invariant (LTI) dynamical system.
I will present numerical methods for MEPs and show how we can apply them so solve RMEPs numerically by transformations into standard MEPs. In some cases, this approach seems computationally more attractive than the block Macaulay method, the only other currently available numerical method for RMEPs.
This talk is based on joint work with Michiel Hochstenbach and Tomaž Košir.
