Flip Graphs with Symmetry and New Matrix Multiplication Schemes

Gaussian elimination is not optimal

Volker Strassen · 1969

Earlier work this paper cites.

Algorithms for matrix multiplication

Richard P. Brent · 1970

Earlier work this paper cites.

On minimizing the number of multiplications necessary for matrix multiplication

J. E. Hopcroft and L. R. Kerr · 1971

Earlier work this paper cites.

A noncommutative algorithm for multiplying 3 × 3 3\times 3 matrices using 23 multiplications

Julian D. Laderman · 1976

Earlier work this paper cites.

On varieties of optimal algorithms for the computation of bilinear mappings i. the isotropy group of a bilinear mapping

Hans F. de Groote · 1978

Earlier work this paper cites.

On varieties of optimal algorithms for the computation of bilinear mappings ii. optimal algorithms for 2 × 2 2\times 2 -matrix multiplication

Hans F. de Groote · 1978

Earlier work this paper cites.

Matrix multiplication via arithmetic progressions

Don Coppersmith and Shmuel Winograd · 1990

Earlier work this paper cites.

Optimization techniques for small matrix multiplication

Charles-Éric Drevet, Md. Nazrul Islam, and Éric Schost · 2011

Earlier work this paper cites.

The bilinear complexity and practical algorithms for matrix multiplication

Alexey V. Smirnov · 2013

Cited alongside, same era.

Modern Computer Algebra

Joachim von Zur Gathen and Jürgen Gerhard · 2013

Cited alongside, same era.

Symmetries of matrix multiplication algorithms. i, 2015

V. P. Burichenko · 2015

Cited alongside, same era.

Matrix multiplication algorithms from group orbits, 2016

Joshua A. Grochow and Cristopher Moore · 2016

Cited alongside, same era.

A non-commutative algorithm for multiplying (7 x 7) matrices using 250 multiplications

Alexandre Sedoglavic · 2017

Cited alongside, same era.

The geometry of rank decompositions of matrix multiplication ii: 3 × 3 matrices

Grey Ballard, Christian Ikenmeyer, J.M. Landsberg, and Nick Ryder · 2019

Cited alongside, same era.

On automorphism group of a possible short algorithm for multiplication of 3 × 3 3\times 3 matrices, 2022

Vladimir Burichenko · 2022

Later among the works it cites.

Discovering faster matrix multiplication algorithms with reinforcement learning

Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert, Bernardino Romera-Paredes, Mohammadamin Barekatain, Alexander Novikov, Francisco J. R. Ruiz, Julian Schrittwieser, Grzegorz Swirszcz, David Silver, Demis Hassabis, and Pushmeet Kohli · 2022

Later among the works it cites.

Flip graphs for matrix multiplication

Manuel Kauers and Jakob Moosbauer · 2023

Later among the works it cites.

Yet another catalogue of fast matrix multiplication algorithms

Alexandre Sedoglavic · 2023

Later among the works it cites.

Adaptive flip graph algorithm for matrix multiplication

Yamato Arai, Yuma Ichikawa, and Koji Hukushima · 2024

Later among the works it cites.

More asymmetry yields faster matrix multiplication