They propose to develop a number of parallel algorithms for the new multicluster CEDAR computer. The research will cover algorithms and methods that are used in important areas in scientific computing. The parallel algorithms will not only be targeted for the CEDAR computer architecture but also for other shared memory multiprocessor computers possessing hierarchical memories. The topics to be covered are: (i) solution of general large sparse systems of linear and nonlinear equations; (ii) solution of large sparse eigenvalue problems; and (iii) rapid elliptic solvers.