Neurodynamic analysis for the Schur decomposition of the box problems

Neurodynamic analysis for solving the Schur decomposition of the box problems is presented in this paper. By constructing a number of dynamic systems, all the eigenvectors of a given matrix pair (A,B) can be searched and thus the decomposition realized. Each constructed dynamical system is demonstrated to be globally convergent to an exact eigenvector of the matrix box pair (A,B). It is also demonstrated that the dynamical systems are primal in the sense of the neural trajectories never escape from the feasible region when starting at it. Compared with the existing neural network models for the generalized eigenvalue problems, the proposed neurodynamic approach has two advantages: 1) it can find all the eigenvectors and 2) all the proposed systems globally converge to the problem's exact eigenvectors.