How to execute a nested loop in band parallelism on a multiprocessor system is addressed. The mathematical models of the waveband method, the hyperplane method, the modified hyperplane method and the linear band method are derived and compared. Since the structures of the real multiprocessor systems are at most 3-dimensional, in order to map the loop into these systems, an efficient algorithm for finding the optimal linear band in 2-dimensional index space, instead of a high dimensional index space, is proposed.

A new approach toward robust parameter estimation is presented. As opposed to schemes based on classical saddlepoint techniques, the methods apply quite naturally to dependent and/or nonstationary data and also have the advantage of providing a quantitative measure of the degree of robustness offered by a particular estimator. It is shown why censoring observations of large magnitude does indeed impart robustness, and it also shown how nontraditional schemes have certain advantages, particularly when trading off performance and robustness. The application of the results is further demonstrated by including several illustrative examples.>