A parallel algorithm for the diagonalization of symmetric matrices and itsneural network implementation.

A neural network that is capable of solving the eigensystem problem for sym metric matrices is presented. Following the idea of the Givens rotator, we extend the concept of parallel rotation proposed in (Watkins, 1991), where only rotations over independent planes are considered. In this paper we pre sent il neural network algorithm that can find the rotation angles over all possible planes simultaneously. An array of neurons is responsible of find ing the rotation angle for each plane, This array is called a neural rotato r, The input-output relation of the neural rotator. is analyzed and an inte resting consequence of the use of neurons with bounded exponential and loga rithm outputs appears: the eigenvalues of the system will be ordered once t he algorithm converges. Each neural rotator has a term that is conserved, t hat is, the present rotation angle is taken into account in the calculation of the next rotation angle. Simulations done with our algorithm, called EI GEN-NET, show that an important gain in performance is obtained in comparis on with the traditional Givens rotation method.