Efficient algorithms for massively parallel computers

The authors investigate the stability of massively parallel computations using a linear systems approach. Stability is important for several reasons. These include bounding the response of the algorithm to numerical noise so that the typically small amount of local memory can be used efficiently, as well as designing algorithms and even hardware to be fault tolerant. Both Lyapunov stability (insensitivity to small changes in data and to noise) and structural stability (fault tolerance in hardware and software) are studied. The methodology is motivated by neural network modeling but may have larger applications