Information processing with lossless cellular neural networks

The eigenvalues of a symmetric tridiagonal matrix can be computed via an iterative diagonalization with the aid of the QR-algorithm. Interpolating the matrices of subsequent iteration steps with continuous (time) trajectories leads to the concept of matrix flows on manifolds. This can be viewed as the transients of a nonlinear dynamical system. Taking samples from the continuous trajectories results exactly in the matrices given by the iteration steps of the discrete algorithm. Thus, in the fixed point of the dynamical system, the desired eigenvalues are found. This could be used as basis for nonlinear filtering operations based on sorting. Mapping these nonlinear ODE's onto physical structures, lossless nonlinear dynamical circuits are obtained.