2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1986)

Oct. 27, 1986 to Oct. 29, 1986

ISSN: 0272-5428

ISBN: 0-8186-0740-8

pp: 49-54

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/SFCS.1986.52

ABSTRACT

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 indications of proofs, if any. Detailed arguments may be found in 26,27.

INDEX TERMS

CITATION

V. Strassen,
"The asymptotic spectrum of tensors and the exponent of matrix multiplication",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 49-54, 1986, doi:10.1109/SFCS.1986.52