Solving Linear Systems by a Neural Network Canonical Form of Efficient Gradient Descent

In this paper the authors describe a novel terminal attractor algorithm for solving linear systems, named ELISA. The method here presented is based on a special neural network continuous form of gradient descent, approaching the minimum of a quadratic function in a constant time, depending solely on the initial value of the residual function. The algorithm is founded on a new concept, called non-suspiciousness, which can be seen as a generalisation of convexity. Under general hypotheses it is proven that ELISA has a quadratic computational complexity and therefore is theoretically optimal. The preliminary numerical experiences clearly assess ELISA's efficiency both by dominant operation counting and in terms of CPU-time.