Consequences of the Moosbauer-Poole Algorithms
Manuel Kauers, Isaac Wood
TL;DR
This paper explores improved matrix multiplication algorithms for various rectangular matrices, building on recent schemes that reduce the number of multiplications needed for 5x5 and 6x6 matrices.
Contribution
It introduces new optimized matrix multiplication schemes for rectangular matrices using flip graph search, improving upon recent minimal multiplication counts.
Findings
Reduced the number of multiplications for specific rectangular matrices.
Developed new algorithms based on flip graph search.
Enhanced efficiency of matrix multiplication schemes.
Abstract
Moosbauer and Poole have recently shown that the multiplication of two matrices requires no more than 93 multiplications in the (possibly non-commutative) coefficient ring, and that the multiplication of two matrices requires no more than 153 multiplications. Taking these multiplication schemes as starting points, we found improved matrix multiplication schemes for various rectangular matrix formats using a flip graph search.
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Taxonomy
TopicsPolynomial and algebraic computation · Tensor decomposition and applications · Cryptography and Residue Arithmetic