It is noted that the training of feedforward networks using the conventional backpropagation algorithm is plagued by poor convergence and misadjustment. The authors introduce the multiple extended Kalman algorithm (MEKA) to train feedforward networks. It is based on the idea of partitioning the global problem of finding the weights into a set of manageable nonlinear subproblems. The algorithm is local at the neuron level. The superiority of MEKA over the global extended Kalman algorithm in terms of convergence and quality of solution obtained on two benchmark problems is demonstrated. The superior performance can be attributed to the nonlinear localized approach. In fact, the nonconvex nature of the local performance surface reduces the chances of getting trapped into a local minima

It is shown that the (scaled) conditional moments of performability in Markov models are the states of a cascaded, linear, continuous-time dynamic system with identical system matrices in each stage. This interpretation leads to a simple method of computing the first moment for nonhomogeneous Markov models with finite mission time. In addition, the cascaded system representation leads to the derivation of a set of two stable algorithms for propagating the conditional moments of performability in homogeneous Markov models. In particular, a very fast doubling algorithm using diagonal Pade approximation to compute the matrix exponential and repeated squaring is derived. The algorithms are widely recognized, to be superior to those based on eigenvalue analysis in terms of both the computational efficiency and stability. The algorithms have obvious implications in solving reliability/availability models with large mission times.>

A fast version of the packpropagation algorithm based on the recursive least squares (RLS) technique is introduced. The added storage requirement and computation associated with RLS can be easily incorporated into the network architecture, and consequently the algorithm is still local. The enhanced algorithm performs consistently better than the backpropagation algorithm in a set of simulations involving two benchmark problems.>