Relative convergence estimates for the spectral asymptotic in the Large Coupling Limit

2009/02/13 by Luka Grubišić, Grubisic, Luka
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0902.2287

openalex publication_date 2009/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational Linear Algebra to obtain estimates even for eigenvalues which are in gaps of the essential spectrum. Further, we also identify a class of "regular" stiff perturbations with (provably) good asymptotic properties. The Arch Model from the theory of elasticity is presented as a prototype for this class of perturbations. We also show that we are able to study model problems which do not satisfy this regularity assumption by presenting a study of a Schroedinger operator with singular obstacle potential.

Citations

• The Rotation of Eigenvectors by a Perturbation. III
• Elementary linear algebra for advanced spectral problems

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