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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 845459, 8 pages
Research Article

A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems

School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, P.O. Box 101, Beijing 100876, China

Received 12 May 2013; Revised 18 July 2013; Accepted 1 August 2013

Academic Editor: Chang-Hua Lien

Copyright © 2013 Xin-long Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented.