Parallel matrix-multiplication algorithm for distributed parallel computers

Abstract

This paper proposes a matrix-multiplication algorithm suited to the distributed computer environment. The system is implemented using PVM and the execution time is evaluated. One of the conventional methods implemented using PVM is the systolic method. However, this method is limited with respect to the matrix size that can be calculated and the number of computers that can be used in the calculation. This paper first extends the algorithm so that these limitations are lifted. Then, an algorithm is proposed which can reduce the communication complexity, although the computational complexity is slightly increased. These two algorithms are implemented using PVM, and the execution time is measured. In either algorithm, an acceleration rate exceeding the number of computers is obtained. The effectiveness is found to be due to the effect of the cache memory, and the speed improvement obtained by using cache memory is investigated. The optimal number of matrix divisions from the viewpoint of cache memory size is also discussed. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 36(4): 48–59, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10551