Inverse Iteration for Laplace Eigenvalue Problems

Abstract: The spectrum of the Laplacian operator is an important object in the analysis of PDEs which depends on the domain and on the boundary conditions. The smallest ("principal") eigenvalue admits a useful variational characterization in terms of the Rayleigh quotient of the operator. We can adapt inverse iteration, an iterative technique for computing eigenvalues of symmetric PD matrices, to the infinite-dimensional setting. In this talk we will outline the application of inverse iteration for to various boundary value problems for Poisson's equation, as well as a related problem in optimal insulation.