A Strassen-like matrix multiplication suited for squaring and higher power computation

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.