The optimal number of field operations needed to multiply two square n × n matrices up to constant factors is still unknown. This is a major open question in theoretical computer science. As of January 2024, the best bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.371552).
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Abstract: The main results of this paper have the following flavor: given one algorithm for multiplying matrices, there exists another, better, algorithm.
Abstract. The number of essential multiplications required to multiply matrices of size N×N and N×Nx is studied as a function f(x). Bounds to f(x) sharper than ...
The main results of this paper have the following flavor: Given one algorithm for multiplying matrices, there exists another, better, algorithm.
The main results of this paper have the following fla- vor: given one algorithm for multiplying matrices, there exists another, better, algorithm.
If multiplication of two n × n matrices can be obtained in O(nα) operations, the least upper bound for α is called the exponent of matrix multiplication and is ...
The main results of this paper have the following flavor: given one algorithm for multiplying matrices, there exists another, better, algorithm.
The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and ...
As of April 2024, the best announced bound on the asymptotic complexity of a matrix multiplication algorithm is O(n2.371552) time, given by Williams, Xu, Xu, ...
The main results of this paper have the following flavor: Given one algorithm for multiplying matrices, there exists another, better, algorithm.