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2005•Journal of Jinan UniversityRequires access

An improved method for general perturbation eigenvalue problems

Sun Hui

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Abstract

An improved perturbation method for general eigenvalue problems is presented. The proposed method is universally applicable to all the three cases of eigenvalue problems: distinct, repeated and nearly equal eigenvalues. The improvement is made to the orthogonal and normality condition and the solving condition of the eigenvector coefficient matrix adopted in the existing methods. Illustrative examples are given to demonstrate the precision of the improved technique.

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What this paper is about

An improved perturbation method for general eigenvalue problems is presented. The proposed method is universally applicable to all the three cases of eigenvalue problems: distinct, repeated and nearly equal eigenvalues. The improvement is made to the orthogonal and normality condition and the solving condition of the eigenvector coefficient matrix adopted in the existing methods. Illustrative examples are given to demonstrate the precision of the improved technique.

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Available abstract

An improved perturbation method for general eigenvalue problems is presented. The proposed method is universally applicable to all the three cases of eigenvalue problems: distinct, repeated and nearly equal eigenvalues. The improvement is made to the orthogonal and normality condition and the solving condition of the eigenvector coefficient matrix adopted in the existing methods. Illustrative examples are given to demonstrate the precision of the improved technique.

Key concepts: Eigenvalues and eigenvectors, Eigenvalue perturbation, Normality, Perturbation (astronomy), Mathematics, Applied mathematics, Divide-and-conquer eigenvalue algorithm, Inverse iteration

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