Displaying similar documents to “Eigenvalues of a Linear Transformation”

Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators

Andrey Andreev, Milena Racheva (2014)

Applications of Mathematics

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This article presents an idea in the finite element methods (FEMs) for obtaining two-sided bounds of exact eigenvalues. This approach is based on the combination of nonconforming methods giving lower bounds of the eigenvalues and a postprocessing technique using conforming finite elements. Our results hold for the second and fourth-order problems defined on two-dimensional domains. First, we list analytic and experimental results concerning triangular and rectangular nonconforming elements...

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

Khelifi, Abdessatar (2005)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 35J05, 35C15, 44P05 In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is jointly holomorphic...