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
Computational complexity and numerical stability
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Algorithms for matrix multiplication
Algorithms for matrix multiplication
A New Algorithm for Inner Product
IEEE Transactions on Computers
On Efficient Computation of Matrix Chain Products
IEEE Transactions on Computers
A Simple Approach to the Error Analysis of Division-Free Numerical Algorithms
IEEE Transactions on Computers
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The error complexity analysis of three algorithms for matrix multiplication and matrix chain product has been given. It is shown that the usual inner product type algorithm is by far the best algorithm for simple matrix multiplication or matrix chain product in terms of minimal basic term growth and minimal error complexities, the latter being independent of the order of pairwise matrix multiplications. Winograd's algorithm is comparable to the usual one, although in matrix chain product the error and data complexities are very sensitive to the order of pairwise matrix multiplication. Strassen's algorithm is not very attractive numerically for having the largest upper bound for both the maximum error complexity and the number of basic terms generated.