Stable Computation of Laplacian Eigenfunctions Corresponding to Clustered Eigenvalues

2025/06/09 by Ryoki Endo, Xuefeng Liu, Endo, Ryoki +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2506.07340

Abstract

The accurate computation of eigenfunctions corresponding to tightly clustered Laplacian eigenvalues remains an extremely difficult problem. In this paper, using the shape difference quotient of eigenvalues, we propose a stable computation method for the eigenfunctions of clustered eigenvalues caused by domain perturbation.

Citations

• The Second Dirichlet Eigenvalue is Simple on Every Non-equilateral Triangle, Part II: Nearly Equilateral Triangles
• The Rotation of Eigenvectors by a Perturbation. III

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