2000•Chinese Journal of ComputersRequires access

Computing Eigenvalues and Eigenvectors of Matrix by Neural Networks

Yi Zhang

Abstract

A class of neural networks described by differential equations is employed to compute out all eigenvalues and eigenvectors of any real symmetric matrix. Structure for the set of equilibrium points of the network is studied in detail. The differential equation of the network is solved by solving a simple one dimensional differential equation. Solutions of the network are represented by the eigenvalues and eigenvectors of the symmetric matrix, and the asymptotic behavior of the solutions is analyzed. Finally, a algorithm for computing all eigenvalues and eigenvectors of real symmetric matrix is proposed.

About this research paper

What this paper is about

Why it matters

OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Matrix differential equation, Eigenvalues and eigenvectors, Defective matrix, Spectrum of a matrix, Eigenvalue perturbation, Mathematics, Modal matrix, Eigenvalues and eigenvectors of the second derivative