# Powers of Tensors and Fast Matrix Multiplication

arXiv: https://arxiv.org/abs/1401.7714 · HTML: https://mlsanity.com/paper/1401.7714/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2014.

## Built on by (most cited first, 11 of 11)

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- [Matrix Multiplication: Verifying Strong Uniquely Solvable Puzzles](https://mlsanity.com/paper/2301.00074/) (2022)
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## Abstract (arXiv)

This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic constructions also called a 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 ω<2.3728639 on the exponent of square matrix multiplication, which slightly improves the best known upper bound.