Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system

Abstract

The known fast sequential algorithms for multiplying two N N matrices (over an arbitrary ring) have time complexity O(N), where 2 < < 3. The current best value of is less than 2.3755. We show that for all 1 p N , m ultiplying two N N matrices can be performed on a p-processor linear array with a recon gurable pipelined bus system (LARPBS) in O N p + N 2 p 2= log p time. This is currently the fastest parallelization of the best known sequential matrix multiplication algorithm on a distributed memory parallel system. In particular, for all 1 p N 2:3755 , m ultiplying two N N matrices can be performed on a p-processor LARPBS in O N 2:3755 p + N 2 p 0:8419 log p time, and linear speedup can be achieved for p as large as O(N 2:3755 =(log N) 6:3262). Furthermore, multiplying two N N matrices can be performed on an LARPBS with O(N) processors in O(log N) time. This compares favorably with the performance on a PRAM.

A New Parallel Algorithm for EREW PRAM Matrix Multiplication

“…Specially a systematic design of cylindrical array for matrix multiplication have been presented. Keqin Li et al presented a brief material on parallel matrix multiplication with a reconfigurable pipelined bus system [9]. They claimed that for multiplication of 2 matrices of order can be done in time.…”

Matrix product on heterogeneous master-worker platforms

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Scalable Parallel Matrix Multiplication on Distributed Memory Parallel Computers

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