Faster Algorithms for Rectangular Matrix Multiplication

  title={Faster Algorithms for Rectangular Matrix Multiplication},
  author={François Le Gall},
  journal={2012 IEEE 53rd Annual Symposium on Foundations of Computer Science},
Let α be the maximal value such that the product of an n × n<sup>α</sup> matrix by an n<sup>α</sup> × n matrix can be computed with n<sup>2+o(1)</sup> arithmetic operations. In this paper we show that α >; 0.30298, which improves the previous record α >; 0.29462 by Coppersmith (Journal of Complexity, 1997). More generally, we construct a new algorithm for multiplying an n × n<sup>k</sup> matrix by an n<sup>k</sup> × n matrix, for any value k ≠ 1. The complexity of this algorithm is better than… CONTINUE READING
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