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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
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.
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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
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