Approximation methods for nonlinear eigenvalue problems - Erik Lindgren (KTH Royal Institute of Technology, Sweden)

Abstract

In this talk, I will discuss two novel methods for approximating extremals
of "nonlinear" Rayleigh quotients. The first approximation scheme is based on the
method of inverse iteration for square matrices. The second method is based
on the large time behavior of solutions of a doubly nonlinear evolution, corresponding
to the heat equation in the case of the eigenvalue problem for
the Laplace operator. Both schemes have the property that the
Rayleigh quotient is nonincreasing along solutions and that properly scaled
solutions converge to an extremal of the Rayleigh quotient. I will focus on
concrete examples in Sobolev spaces where our results apply.

The talk is based on joint work with Ryan Hynd (University of Pennsylvania).