Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions
Analysis of PDEs
2025-06-03 v2
Abstract
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.
Cite
@article{arxiv.2408.05197,
title = {Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions},
author = {Benjamin Lyons and Emily Ruttenberg and Nicholas Zitzelberger},
journal= {arXiv preprint arXiv:2408.05197},
year = {2025}
}