This research concerns the numerical solution of large sparse linear systems of equations arising from the discretization of partial differential equations. A particular emphasis is on preconditioned conjugate gradient methods and, in particular, ways of making SSOR and incomplete Choleski preconditioning more effective on parallel and vector computers. Some of the possibilities to be considered are: further development of the many color approach to approximating the natural ordering while maintaining adequate parallelism; further development of the diagonal ordering approach for the natural ordering; development of preconditioners for the reduced system conjugate gradient method. The primary model problems are three- dimensional Poisson-type equations. The primary machines to be used are the CRAY-2 and Y-MP, and Intel and Ncube hypercubes.
