Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions
Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions
Inverse iteration is a tool used in operator theory to investigate the spectral properties of a linear operator. We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal eigenfunction and show that the corresponding Rayleigh quotients converge to the principal eigenvalue. We also propose a related iterative method for an eigenvalue problem arising from a model for optimal insulation and provide some partial results.
This presentation is based on a project that I conducted with Benjamin Lyons (Rose-Hulman Institute of Technology), and Ephraim Ruttenberg (University of Maryland Baltimore County), under the mentorship of Farhan Abedin (Lafayette College) and Jun Kitagawa (Michigan State University).