Approximation methods for nonlinear eigenvalue problems

Erik Lindgren (KTH, Stoccolma)

10/05/2017, ore 12, aula 3

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).