On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication
arXiv:1509.083231.210 citations
Originality Synthesis-oriented
AI Analysis
For researchers in algebraic complexity, this work offers a complete geometric understanding of border rank for a specific small matrix multiplication case, but is incremental in nature.
The paper provides a detailed geometric analysis of border rank algorithms for multiplying an n×2 matrix by a 2×2 matrix, characterizing the optimal border rank and the structure of minimal algorithms.
We make an in-depth study of the known border rank (i.e. approximate) algorithms for the matrix multiplication tensor encoding the multiplication of an n x 2 matrix by a 2 x 2 matrix.