AN EFFICIENT PARALLEL IMPLEMENTATION OF A LEAST-SQUARES PROBLEM

Least squares solutions are a very important problem, which appear in a broad range of disciplines (for instance, control systems, optimisat ion, statistics, signal processing). Our interest in this kind of prob lem lies in their use for training neural network controllers. We have recently proposed a new learning algorithm for training multilayer pe rceptrons, in which two least squares problems have to be solved in ea ch iteration. As one of them constitutes the bulk of the computation o f the learning algorithm, we have looked for efficient parallel soluti ons for least squares problems. For accuracy reasons, a QR algorithm w as used to compute these steps of the learning algorithm. By modifying the sequence of operations that are performed by a known parallel sol ution for this type of problem, a boost in parallel efficiency was obt ained. Extensive testing with different topologies and different route r algorithms was conducted, enabling us to determine an optimal soluti on.