Abstract

This paper considers the computation of matrix chain products of the form $M_1 \times M_2 \times \cdots \times M_{n - 1} $. If the matrices are of different dimensions, the order in which the matrices are computed affects the number of operations. An optimum order is an order which minimizes the total number of operations. Some theorems about an optimum order of computing the matrices have been presented in Part I [SIAM J. Comput., 11 (1982), pp. 362–373]. Based on those theorems, an $O(n\log n)$ algorithm for finding the optimum order is presented here.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975x+470
2.
S. S. Godbole, An efficient computation of matrix chain products, IEEE Trans. Computers, C-22 (1973), 864–866
3.
Ellis Horowitz, Sartaj Sahni, Fundamentals of computer algorithms, Computer Science Press, Rockville, Md., 1978xiv+626
4.
T. C. Hu, M. T. Shing, Computation of matrix chain products, 1981 Army Numerical Analysis and Computer Conferences, 1981, February
5.
T. C. Hu, M. T. Shing, An O(n) algorithm to find a near-optimum partition of a convex polygon, J. Algorithms, to appear
6.
T. C. Hu, M. T. Shing, Computation of matrix chain products. I, SIAM J. Comput., 11 (1982), 362–373
7.
T. C. Hu, M. T. Shing, Computation of matrix chain products, Part I, Part II, Report, STAN-CS-81-875, Stanford Univ., Stanford, CA, 1981, Sept.

Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 228 - 251
ISSN (online): 1095-7111

History

Submitted: 4 August 1981
Accepted: 7 February 1983
Published online: 13 July 2006

Authors

Affiliations

Metrics & Citations

Metrics

Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited By

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share on social media