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The problem, of finding extreme eigenvalues and eigenvectors of a real symmetric positive definite matrix can be viewed as a smooth optimization problem on a smooth manifold. We present a cost function approach for computing higher dimensional sub-spaces corresponding to smallest and largest eigenvalues simultaneously. This approach is then generalized to develop dynamical system for computing the...
In this paper, we extend the neural network based approaches, which can asymptotically compute the largest or smallest eigenvalues and the corresponding eigenvectors of real symmetric matrix, to the real antisymmetric matrix case. Given any n-by-n real antisymmetric matrix, unlike the previous neural network based methods that were summarized by some ordinary differential equations (ODEs) with 2n...
This paper investigates the stability and boundary of a swarm with a general directed and weighted topology. The stability of a swarm is generally considered as cohesiveness. We construct a symmetric eigenmatrix and define an orthogonal eigenparameter which reflects the degree of orthogonality between the left eigenvector of the coupling matrix corresponding to its zero eigenvalue and the eigenvectors...
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