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, optimisation, statistics, signal processing). Our interest in this kind of problem lies in their use for training neural network controllers. We have recently proposed a new learning algorithm for training multilayer perceptrons, in which two least squares problems have to be solved in each iteration. As one of them constitutes the bulk of the computation of the learning algorithm, we have looked for efficient parallel solutions for least squares problems. For accuracy reasons, a QR algorithm was used to compute these steps of the learning algorithm. By modifying the sequence of operations that are performed by a known parallel solution for this type of problem, a boost in parallel efficiency was obtained. Extensive testing with different topologies and different router algorithms was conducted, enabling us to determine an optimal solution.