Real-time computation of the eigenvector corresponding to the smallest eigenvalue of a positive definite matrix

In the real-time applications of many signal processing algorithms, such as the TLS (Total Least Squares) algorithm, it is desired to compute as fast as possible the eigenvector corresponding to the smallest eigenvalue of a positive definite matrix. This paper proposes an analog circuit approach to computing in real-time the desired eigenvector. We show analytically and by simulations that the proposed circuit is guaranteed to be stable and to provide the results arbitrarily close to the accurate eigenvector within an elapsed time of only a few characteristic time constants of the circuit.