Neural network algorithms based on the QR decomposition method of least squares

We present a set of algorithms for feed-forward multilayer neural networks based on the QR and the inverse-QR recursive least-squares algorithms. These algorithms possess excellent numerical stability, fast convergence characteristics compared to the backpropagation algorithm and require much fewer iterations to train the neural networks. We apply these algorithms to practical problems of pattern recognition of different patterns and also for optimization with excellent results. We compare these algorithms with the previously reported ones which are also based on the least squares method and found the one based on the inverse QR method to be superior to the others. The computational complexity comparison of these algorithms is also presented