Addition requirements for matrix and transposed matrix products
Journal of Algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
GEMMW: a portable level 3 BLAS Winograd variant of Strassen's matrix-matrix multiply algorithm
Journal of Computational Physics
On the additive complexity of 2 x 2 matrix multiplication
Information Processing Letters
On Winograd's Algorithm for Inner Products
IEEE Transactions on Computers
Adaptive Winograd's matrix multiplications
ACM Transactions on Mathematical Software (TOMS)
Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
The Journal of Supercomputing
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Strassen's method is not the asymptotically fastest known matrix multiplication algorithm, but it is the most widely used for large matrices. Since his manuscript was published, a number of variants have been proposed with different addition complexities. Here we describe a new one. The new variant is at least as good as those already known for simple matrix multiplication, but can save operations either for chain products or for squaring. Moreover it can be proved optimal for these tasks. The largest saving is shown for nth-power computation, in this scenario the additive complexity can be halved, with respect to original Strassen's.