Abstract
We present efficient parallel matrix multiplication algorithms for linear arrays with reconfigurable pipelined bus systems (LARPBS). The main contributions are as follows. We develop five matrix multiplication algorithms with varying degrees of parallelism on the LARPBS computing model, namely, MM1, MM2, MM3, and compound algorithms C 1(ε) and C 2(δ). Algorithm C 1(ε) has adjustable time complexity in sub-linear level. Algorithm C 2(δ) implies that it is feasible to achieve sub-logarithmic time using o(N 3) processors for matrix multiplication on a realistic system. Algorithms MM3, C 1(ε), and C 2(δ) all have o(N 3) cost, and hence, are very processor efficient. Algorithms MM1, MM3, and C 1(ε) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM2 and C 2(δ) are applicable to array elements that are integers of bounded magnitude, or floating-point values of bounded precision and magnitude, or boolean values. Extension of algorithms MM2 and C 2(δ) to unbounded integers and reals, as well as the application of our matrix multiplication algorithms in solving a number of important and fundamental matrix computation problems, are also discussed.
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Li, K. (1998). Fast Matrix Multiplication and Related Operations Using Reconfigurable Optical Buses. In: Li, K., Pan, Y., Zheng, S.Q. (eds) Parallel Computing Using Optical Interconnections. The Springer International Series in Engineering and Computer Science, vol 468. Springer, Boston, MA. https://doi.org/10.1007/978-0-585-27268-9_12
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DOI: https://doi.org/10.1007/978-0-585-27268-9_12
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