Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions

2024/08/09 by Lyons, Benjamin, Ruttenberg, Emily, Zitzelberger, Nicholas
#35A35 #35J25 #47A75 #49R05 #65N25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.05197

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.

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