Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers
Iterative methods for the solution of tridiagonal systems are considered, and a new iteration is presented, whose rate of convergence is comparable to that of the optimal two-cyclic Chebyshev iteration but which does not require the calculation of optimal parameters. The convergence rate depends only on the magnitude of the elements of the tridiagonal matrix and not on its dimension or spectrum. The theory also has a natural extension to block tridiagonal systems. Numerical experiments suggest that on a parallel computer this new algorithm is the best of the iterative algorithms considered.
Determining whether a new software development technique is useful and usable is a challenging taste. Various flavors of empirical study may be used to help with this task, including surveys, case studies, and experiments. Little guidance is available within the software engineering community to help choose among these alternatives when assessing a new and evolving software development technique within some cost bounds. We faced this challenge when assessing a new programming technique called aspect-oriented programming. To assess the technique, we chose to apply both a case study approach and a series of four experiments because we wanted to understand and characterize the kinds of information that each approach might provide. We describe and critique the evaluation methods we employed, and discuss the lessons we have learned. These lessons are applicable to other researchers attempting to assess new programming techniques that are in an early stage of development.