## Continuous methods for extreme and interior eigenvalue problems

- G. H. Golub, L.-Z. Liao
- LAA, Vol. 415, pp. 31-51
- 2006

1 Excerpt

- Published 2007 in 2007 International Conference on Computational…

This paper presents neurodynamic analysis for solving symmetric Schur decomposition problems. A series of dy- namical systems are proposed for finding the orthogonal decomposition matrix X for a given symmetric matrixA which are demonstrated to converge to the rows of the ma- trix X. It is also demonstrated that all the dynamical sys- tems are invariant in the sense that the system's trajectories will never escape from feasible region of an optimization problem when starting at it. By constructing a well-defined energy function corresponding to a dynamical system, it is shown that the orthogonal decomposition matrix X can be realized by the proposed dynamical systems. The theoretic analysis given here shows that the neurodynamic method is an alternative promising approach for solving the symmet- ric Schur decomposition problems.

@article{Zhang2007NeurodynamicAF,
title={Neurodynamic Analysis for Symmetric Schur Decomposition Problems},
author={Quanju Zhang and Yi Niu and Yajuan Yang and Wenxue Niu},
journal={2007 International Conference on Computational Intelligence and Security (CIS 2007)},
year={2007},
pages={485-489}
}