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2011•Mathematical Problems in EngineeringOpen access

An Inverse Eigenvalue Problem for Jacobi Matrices

Zhengsheng Wang, Baojiang Zhong

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Abstract

A kind of inverse eigenvalue problem is proposed which is the reconstruction of a Jacobi matrix by given four or five eigenvalues and corresponding eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.

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What this paper is about

A kind of inverse eigenvalue problem is proposed which is the reconstruction of a Jacobi matrix by given four or five eigenvalues and corresponding eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.

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Available abstract

A kind of inverse eigenvalue problem is proposed which is the reconstruction of a Jacobi matrix by given four or five eigenvalues and corresponding eigenvectors. The solvability of the problem is discussed, and some sufficient conditions for existence of the solution of this problem are proposed. Furthermore, a numerical algorithm and two examples are presented.

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

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