PARALLEL REAL-TIME COMPUTATION OF NONLINEAR FEEDBACK FUNCTIONS

Abstract

This paper focuses on the improvement in the quality of computation provided by parallelism. The problem of interest is that of computing the maximum of a nonlinear feedback function in a real-time environment. We show that the solution obtained in parallel is significantly, provably, and consistently better than a sequential one. It is important to note that our purpose is not to demonstrate merely that a parallel computer can obtain a solution to a computational problem that is of higher quality than one derived sequentially. The latter is an interesting (and often surprising) observation in its own right, but we wish to go further. It is shown here that the improvement in quality due to parallelism can be arbitrarily high. To be specific, the ratio of the parallel solution to the sequential one is typically superlinear in the number of processors used by the parallel computer. This result is akin to superlinear speedup—a phenomenon itself originally thought to be impossible.