The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
On the time required for a sequence of matrix products
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Chain mulitplication of matrices of approximately or exactly the same size
Communications of the ACM
Processor Allocation and Task Scheduling of Matrix Chain Products on Parallel Systems
IEEE Transactions on Parallel and Distributed Systems
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
Error Complexity Analysis of Algorithms for Matrix Multiplication and Matrix Chain Product
IEEE Transactions on Computers
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This paper discusses the computation of matrix chain products of the form M1 × M22 × ··· × Mn where Mi'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 Topt is also presented. In most cases, the algorithm yields the optimal order or an order which takes only a few percent longer than Topt (less than 1 percent on the average).