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2008•Journal of Hefei UniversityRequires access

Inverse Eigenvalue Problem of Jacobi Matrices

Qian Cai

Open publisher page 8 citations

Abstract

On the basis of analyzing some inverse problems in the matrix theory,a kind of inverse eigenvalue problem which is the reconstruction of Jacobi matrix by three eigenvalues and eigenvectors is proposed.By using the conditions for the solvability of the linear equation systems,a sufficient and necessary condition for the solvability of the inverse eigenvalue problem and its solving method are obtained.Furthermore one numerical experiment is given.

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What this paper is about

On the basis of analyzing some inverse problems in the matrix theory,a kind of inverse eigenvalue problem which is the reconstruction of Jacobi matrix by three eigenvalues and eigenvectors is proposed.By using the conditions for the solvability of the linear equation systems,a sufficient and necessary condition for the solvability of the inverse eigenvalue problem and its solving method are obtained.Furthermore one numerical experiment is given.

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Available abstract

On the basis of analyzing some inverse problems in the matrix theory,a kind of inverse eigenvalue problem which is the reconstruction of Jacobi matrix by three eigenvalues and eigenvectors is proposed.By using the conditions for the solvability of the linear equation systems,a sufficient and necessary condition for the solvability of the inverse eigenvalue problem and its solving method are obtained.Furthermore one numerical experiment is given.

Key concepts: Eigenvalues and eigenvectors, Mathematics, Inverse, Inverse iteration, Inverse problem, Jacobi eigenvalue algorithm, Divide-and-conquer eigenvalue algorithm, Matrix (chemical analysis)

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