A non-commutative algorithm for multiplying 5x5 matrices using 99 multiplications

Gaussian elimination is not optimal

Strassen, V · 1969

Earlier work this paper cites.

On minimizing the number of multiplication necessary for matrix multiplication

Hopcroft, J. E., and Kerr, L. E · 1971

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A non-commutative algorithm for multiplying 3 × 3 3\times 3 matrices using 23 23 multiplications

Laderman, J. B · 1976

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A non-commutative algorithm for multiplying 5 × 5 {5\times 5} matrices using 103 103 multiplications

Schachtel, G · 1978

Earlier work this paper cites.

How can we speed up matrix multiplication?

Pan, V. Y · 1984

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On transformations of algorithms to multiply 2 × 2 {2\times 2} matrices

Chatelin, Ph · 1986

Cited alongside, same era.

A non-commutative algorithm for multiplying 5 × 5 {5\times 5} matrices using 102 102 multiplications

Makarov, O. M · 1986

Cited alongside, same era.

A non-commutative algorithm for multiplying 5 × 5 {5\times 5} matrices using one hundred multiplications

Makarov, O. M · 1987

Cited alongside, same era.

A group-theoretic approach to fast matrix multiplication

Cohn, H., and Umans, C · 2003

Cited alongside, same era.

Optimization techniques for small matrix multiplication

Drevet, C.-É., Nazrul Islam, M., and Schost, É · 2010

Cited alongside, same era.

Fast matrix multiplication database

Sedoglavic, A

Cited in the paper.

Search and test algorithms for triple product property triples

Hedtke, I., and Murthy, S · 2012

Later among the works it cites.

A fast search algorithm for (m,m,m) triple product property triples and application for 5 × 5 {5\times 5} matrix multiplication

Original

Hart, S., Hedtke, I., Müller-Hannemann, M., and Murthy, S · 2013

Later among the works it cites.

Laderman matrix multiplication algorithm can be constructed using Strassen algorithm and related tensor’s isotropies

Original

Sedoglavic, A · 2017

Closest in time.

A non-commutative algorithm for multiplying 7 × 7 {{7}\times{7}} matrices using 250 250 multiplications

Sedoglavic, A · 2017

Closest in time.