• DOI:10.1109/SFCS.1986.52
Corpus ID: 15077423

The asymptotic spectrum of tensors and the exponent of matrix multiplication

@article{Strassen1986TheAS,
  title={The asymptotic spectrum of tensors and the exponent of matrix multiplication},
  author={V. Strassen},
  journal={27th Annual Symposium on Foundations of Computer Science (sfcs 1986)},
  year={1986},
  pages={49-54}
}

V. Strassen

Published 1986

Mathematics, Computer Science

27th Annual Symposium on Foundations of Computer Science (sfcs 1986)

We introduce an asymptotic data structure for the relative bilinear complexity of bilinear maps (tensors). It consists of a compact Hausdorff space Δ together with an interpretation of the tensors under consideration as continuous functions on Δ. The asymptotic rank of a tensor is simply the maximum of the associated function. On the way we present a new method for estimating the exponent ω of matrix multiplication, leading at present to the bound ω ≪ 2.48. The paper gives only brief… CONTINUE READING

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