A neural-type parallel algorithm for fast matrix inversion

摘要

The paper introduces the orthogonalized back-propagation algorithm(OBA), a training procedure for adjusting the weights of a neural-typenetwork used for matrix inversion. In this framework the adjustableweights correspond to the estimate of the inverse of the matrix. Thealgorithm is iterative, in the sense that an initial estimate of thesolution is chosen and then updated according to some error measure.However, it is also a direct algorithm since, it guarantees exactconvergence after n steps, independent of the initial estimate,where n is the dimension of the matrix to be inverted. Themethod can also be directly applied to solving linear equations and tocomputing the pseudoinverse of matrices with full row or column rank.From an optimization point of view, it is shown that the OBA is anoptimal algorithm for minimizing a quadratic least-squares costfunctional