RUI: Finding All Numerical Solutions for Large-Scale Nonlinear Systems of Equations Parallelly and Reliably in a Given Domain

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9503757 Hu This project will investigate efficient parallel algorithms to find all numerical solutions for large-scale nonlinear systems of equations in a given domain with mathematical certainty, even in the presence of uncertainty in the data, roundoff error, and nonlinearities by finite digit computations. The basic algorithm to be used is based on the interval Newton/Generalized bisection method. Parallel algorithms will be implemented on vector processors, shared-memory multiprocessors, and distributed-memory multicomputers. On a vector processor, new data structures will be designed to take full advantage of completely pipelined functional units of vector processors. To speed memory accessing, techniques will be developed to increase cache hit ratio on machines with cache such as the IBM 3090, and to reduce bank conflict on interleaved memory systems such as the CRAY C90. On a shared memory multiprocessor, optimal partitioning schemes will be studied for given nonlinear systems based on two protocols. By overlapping communication and computation, in addition to reducing communication and contention, large speedup is expected. On distributed-memory multicomputers, algorithms on coarse grained SPMP schemes and fine-grained MPMP schemes will be implemented on realistic machines. General sparsity and scalability will be considered in all implementations. ***