Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
ACM Transactions on Mathematical Software (TOMS)
An O(n) algorithm for determining a near-optimal computation order of matrix chain products
Communications of the ACM
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
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We present a different approach to finding an optimal computation order; it exploits both the difference between the size of the matrices and the difference between the number of nonzero elements in the matrices. Therefore, this technique can be usefully applied where the matrices are almost or exactly the same size. We show that using the proposed technique, an optimal computation order can be determined in time O(n) if the matrices have the same size, and in time O(n3) otherwise.