Inverse Iteration for the Laplace Eigenvalue Problem With Robin and Mixed Boundary Conditions - Lyons, Benjamin; Ruttenberg, Ephraim; Zitzelberger, Nicholas (The PUMP Journal of Undergraduate Research, 2025)
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.