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arXiv · 2408.05197

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

Benjamin Lyons·Emily Ruttenberg·Nicholas Zitzelberger
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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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Benjamin Lyons, Emily Ruttenberg, Nicholas Zitzelberger. 2024-08-09. Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions. https://doi.org/10.46787/pump.v8i.4261

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