Continuous methods for extreme and interior eigenvalue problems
- G. H. Golub, L.-Z. Liao
- LAA, Vol. 415, pp. 31-51
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.