Parallel Computing Using Optical Interconnections pp 249-273 | Cite as

# Fast Matrix Multiplication and Related Operations Using Reconfigurable Optical Buses

## 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, MM_{1}, MM_{2}, MM_{3}, 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 MM_{3}, *C* _{1}(*ε*), and *C* _{2}(*δ*) all have *o*(*N* ^{3}) cost, and hence, are very processor efficient. Algorithms MM_{1}, MM_{3}, and *C* _{1}(*ε*) are general-purpose matrix multiplication algorithms, where the array elements are in any ring. Algorithms MM_{2} 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 MM_{2} 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.

## Keywords

Matrix Multiplication Linear Array Array Element Optical Interconnection Relate Operation## Preview

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