Problems will be studied from a broad spectrum of numerical analysis and it will be determined to what extent fast stable algorithms can be derived for parallel computers. Two categories of parallel architectures will be considered: (1) Shared memory multiprocessors (CRAY-X-MP, CRAY-2, ETA-10, Encore Multimax). (2) Distributed memory message passing architectures (NCUBE, Cyberplus). The goals of the research are: (1) To determine the extent to which various advanced architectures can be utilized to speed up computations, (2) To obtain general design techniques that can be used to derive efficient stable algorithms suitable for high sped parallel processing, and (3) To develop robust codes which efficiently implement these algorithms on parallel architectures. The research conducted to date has resulted in the discovery of a design technique for parallelizing a class of iterative methods for solving large sparse linear systems of equations. Efficient parallel algorithms for shared memory machines with memory hierarchy and for message passing machines have been obtained and are faster than previously existing algorithms. 8722260
