Parallel Direct Methods for Solving Banded Linear Systems.
YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE
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This paper proposes several implementations of Gaussian elimination for solving banded linear systems on multiprocessors. Three simple computer architectures are considered a multiprocessor ring, a grid array and a hypercube, This complexity analysis fully accounts for communication delays by using simple mathematical models where both latency and actual transfert times are incorporated. When the number of processors is small relative to the bandwidth of the system a row interleaved implementation of Gaussian elimination algorithm is attractive. Otherwise, a two-dimensional grid is essential for achieving higher speed-up. The hypercube architecture gives the smallest communication latency times. Additional keywords Parallel computers Scientific computing. Author
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