Karl Meerbergen
KU Leuven, Belgium
NEPv: nonlinear eigenvalue problems with eigenvector nonlinearity
1 December, 14h30-15h15
KU Leuven, Department of Electrical Engineering (ESAT)
ELEC B91.100
streaming link: https://eu.bbcollab.com/guest/4d2fa1a98fe8465094230c575de8b5a3
Abstract
The nonlinear eigenvalue problems with eigenvector nonlinearity (NEPv) is a nonlinear eigenvalue problem whose matrix is also dependent on the normalised eigenvector. To date, numerical methods are fixed point iteration methods, variations on the Self Consistent Field iteration (SCF). For polynomial and rational eigenvalue problems, a spectrally equivalent linear eigenvalue problem exists, a so-called linearization. This is not the case, in general, for the NEPv, even when the matrix is polynomial in the eigenvector.
We briefly review numerical methods for solving nonlinear eigenvalue problems and how they can be extended to eigenvector nonlinearities. The first example are a class of rational NEPv, that can be solved via a linear multi-parameter eigenvalue problem. We discuss structure preserving methods. The second example are polynomial eigenvector nonlinearities (PEPv), which can be described by systems of polynomial equations, which are solved by a contour integration method.
