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An Error Bound for Eigenvalue Analysis by Nodal Condensation

Heinrich Voß

Open publisher page 16 citations

Abstract

The nodal condensation is an efficient way of reducing the size of eigenvalue problems to manageable proportions. In this note we use a minimax characterization of the eigenvalues of the exactly condensed (nonlinear) eigenvalue problem to estimate the errors of the eigenvalues of the reduced (linear) problem. The eigenvalue approximations can be improved considerably by the use of the Rayleigh functional of the nonlinear problem.

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What this paper is about

The nodal condensation is an efficient way of reducing the size of eigenvalue problems to manageable proportions. In this note we use a minimax characterization of the eigenvalues of the exactly condensed (nonlinear) eigenvalue problem to estimate the errors of the eigenvalues of the reduced (linear) problem. The eigenvalue approximations can be improved considerably by the use of the Rayleigh functional of the nonlinear problem.

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Available abstract

The nodal condensation is an efficient way of reducing the size of eigenvalue problems to manageable proportions. In this note we use a minimax characterization of the eigenvalues of the exactly condensed (nonlinear) eigenvalue problem to estimate the errors of the eigenvalues of the reduced (linear) problem. The eigenvalue approximations can be improved considerably by the use of the Rayleigh functional of the nonlinear problem.

Key concepts: Eigenvalues and eigenvectors, Minimax, Nonlinear system, Mathematics, Divide-and-conquer eigenvalue algorithm, Applied mathematics, Inverse iteration, NODAL

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