Distributed MIMD multiprocessor system with MicroAda/SuperMicro(TM) for asynchronous concurrent Newton's algorithms

Abstract

This paper presents a pragmatic example of how to use Ada tasks with Add machines such as SuperMicro(TM) for scientific computing. First, a class of asynchronous concurrent Newton's algorithms: Purely-Asynchronous (PAN), Asynchronous (AN), and Semi-Asynchronous (SAN) algorithms are introduced for distributed computing environment. A sufficient condition is shown to guarantee local convergence of these asynchronous algorithms. Moreover, it is proved that the PAN algorithm is linearly convergent, the AN algorithm is super-linearly convergent, and the SAN algorithm is quadratically convergent. The order of convergence depends on the degree of interaction among computing modules. Second, a non-deterministic program for the asynchronous algorithm is provided by using Ada tasks. The asynchronous algorithm/program is superior to the synchronized counterpart with respect to computation speed and reliability. Lastly, this paper describes a way where the asynchronous algorithm/program can be realized as a hierarchic distributed system with Ada machines. A preliminary result is shown with MicroAda/SuperMicro(TM).