A neural network based matrix inversion algorithm

The implementation of a technique first proposed by J.S. Jang et al. in (Neural Information Processing Systems, D.Z. Anderson, Ed., AIP Press, 1988, p.397-401) for the inversion of a matrix is discussed. The inversion is performed by mapping an appropriate energy function onto a fully connected processing architecture (which is similar to a Hopfield neural network). A description is given of the advantages and disadvantages of inverting a matrix in this fashion as compared with more conventional approaches. In particular, the inversion of highly ill-conditioned matrices is examined