Affiliation:
1. Univ. of Alberta, Alberta, Alta., Canada
Abstract
This paper discusses the computation of matrix chain products of the form
M
1
×
M
2
2 × ··· ×
M
n
where
M
i
's are matrices. The order in which the matrices are computed affects the number of operations. A sufficient condition about the association of the matrices in the optimal order is presented. An
O
(
n
) algorithm to find an order of computation which takes less than 25 percent longer than the optimal time
T
opt
is also presented. In most cases, the algorithm yields the optimal order or an order which takes only a few percent longer than
T
opt
(less than 1 percent on the average).
Publisher
Association for Computing Machinery (ACM)
Reference6 articles.
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2. On Efficient Computation of Matrix Chain Products
3. On the time required for a sequence of matrix products
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