Structured trainable networks for matrix algebra

A novel approach to a large variety of matrix algebra problems is proposed. The basic idea is to represent a given problem by a structured network architecture, train the structured network to match some desired patterns, and obtain the solution to the problem from the weights of the resulting structured network. The basic unit used to construct the network is a simple linear multi-input, single-output weighted summer. The training algorithms for the problems are either standard error back-propagation or the modified error back-propagation. Three detailed structured networks and the corresponding training algorithms are presented for matrix LU decomposition, linear equation solving and singular value decomposition, respectively. Extensions to other matrix algebra problems are straightforward. These new approaches use parallel architectures and algorithms, suitable for VLSI realizations; provide robust computations, with no divisions involved in all the calculations, so that they are free of the divide-by-zero problem; and are very general, suitable for most matrix computation and matrix equation-solving problems