9414630 O'Cinneide Computational probability is an area of study that focuses on the application of non-randomized algorithms for analyzing systems that are subject to randomness. Computational probability is a manifestation of the incorporation of computers into society at large, and into science and engineering in particular. This research is concerned with the problems of computational probability, including the methods of phases, decomposition methods, and asymptotic methods. Some fundamental questions regarding the scope of the method of phases will be investigated. Decomposition method will be combined with the method of phases in an attempt to devise a method-of-phases approach to a large systems. A central theme of the research is to bring numerical analysis to bear on computational probability. In particular, the relationship between non-negative arithmetic and the accuracy of certain algorithms in computational probability will be explored. The theoretical aspect of this research will have some impact on applications through the identification of good algorithms and methodologies for solving problems that have some inherent attributes of randomness. On the application side, the work undertaken in this research can be viewed as part of the process of incorporating the use of computers into the design of complex systems.
