Fall 2014

Powers of Tensors and Fast Matrix Multiplication

Wednesday, November 12th, 2014 11:40 am12:30 pm

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This work presents a method to analyze the powers of a given trilinear form (or tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with existing approaches, this method is based on convex optimization, and thus has polynomial-time complexity. As an application, we use this method to study powers of the construction given by Coppersmith and Winograd [Journal of Symbolic Computation, 1990] and obtain the upper bound w<2.3728639 on the exponent of square matrix multiplication, which slightly improves the best known upper bound.