Eigenvalue enclosures

2013/06/22 by Gabriel R. Barrenechea, Barrenechea, Gabriel Raúl, Lyonell Boulton +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1306.5354

openalex publication_date 2013/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with methods for numerical computation of eigenvalue enclosures. We examine in close detail the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a geometrically motivated method developed more recently by Davies and Plum. We extend various previously known results in the theory and establish explicit convergence estimates in both settings. The theoretical results are supported by two benchmark numerical experiments on the isotropic Maxwell eigenvalue problem.

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• On the quality of complementary bounds for eigenvalues

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