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32-processor Cedar system 45 megaﬂops BLAS3 primitives block Cholesky algorithm block Gram-Schmidt building blocks cache memory Cdoall and cdoacross cdoall or cdoacross Cedar Fortran Compiler Cedar Fortran Program Cedar parallel Center for Supercomputing chunk chunk-scheduling common block conﬂict Cray crossbar switch CSRD Notes Number CSRD researchers D. H. Lawrie data Development CSRD Eispack execution Figure Fortran 77 gate array implements gigabytes per second guided self-scheduling hardware cost/complexity high-performance iiiid implements 4 bits inside an sdoall interconnection network large numbers level of parallelism Linpack Llrbana loop iterations loop parallelism LU factorization matrices memory hierarchy Mflops microtasking multiprocessor systems multitasking network delay numerical linear algebra Omega network optimized overhead packet-switched parallel computers parallel loop parallel supercomputing parallelism is explicit port number positive definite present in Cedar processors Research 8 Development routines run-time s_i/steiii scheduling algorithms sharing memory single Cedar cluster Solving Block Tridiagonal speedup Supercomputing Research