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Status: Supported ×Keyword: submultiplicativity ×Clear all

1 claim from 1 paper

1. Computer Science › Complexity and Algorithms in Graphs

   Rank and border rank of Kronecker powers of tensors and Strassen's laser method

   Conner, Gesmundo, Landsberg and Ventura · Computational Complexity · 2021

   The paper shows border rank is multiplicative for Kronecker squares and cubes of the little Coppersmith-Winograd tensor in some ranges, and introduces a skew-symmetric variant that may help the laser method.

   Supported1 claim, checked
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   1. Supported · 71%The authors give new upper bounds on the Waring rank and Waring border rank of the 3×3 determinant, and its square-root tensor shows strict submultiplicative behaviour.“We determine new upper bounds for the (Waring) rank and the (Waring) border rank of $\det_3$, exhibiting a strict submultiplicative behaviour for $T_{skewcw,2}$ which is promising for the laser method.”