Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations
@article{Pan1978StrassensAI,
title={Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations},
author={Victor Y. Pan},
journal={19th Annual Symposium on Foundations of Computer Science (sfcs 1978)},
year={1978},
pages={166-176}
}A new technique of trilinear operations of aggregating, uniting and canceling is introduced and applied to constructing fast linear non-commutative algorithms for matrix multiplication. The result is an asymptotic improvement of Strassen's famous algorithms for matrix operations.
119 Citations
The Technique of Trilinear Aggregating and the Recent Progress in the Asymptotic Acceleration of Matrix Operations
- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1984
Field extension and trilinear aggregating, uniting and canceling for the acceleration of matrix multiplications
- Computer Science20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979
The acceleration of matrix multiplication MM, is based on the combination of the method of algebraic field extension and trilinear aggregating, uniting and canceling and a fast algorithm of O(N2.7378) complexity for N × N matrix multiplication is derived.
Matrix Multiplication, a Little Faster
- Physics
- 2020
Strassen’s algorithm (1969) was the first sub-cubic matrix multiplication algorithm. Winograd (1971) improved the leading coefficient of its complexity from 6 to 7. There have been many subsequent ...
Recursion removal in fast matrix multiplication
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- 2003
A general method of breaking recursions in fast matrix multiplication algorithms is introduced, which is generalized from recursions removal of a specificfast matrix multiplication algorithm of Winograd.
Matrix Multiplication , a Li le Faster Regular Submission
- Computer Science
- 2017
A generalization of Probert’s lower bound that holds under change of basis is proved, showing that for matrix multiplication algorithms with a 2×2 base case, the leading coecient of the Strassen-Winograd algorithm cannot be further reduced, hence optimal.
Multiplying matrices faster than coppersmith-winograd
- Computer ScienceSTOC '12
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An automated approach for designing matrix multiplication algorithms based on constructions similar to the Coppersmith-Winograd construction is developed and a new improved bound on the matrix multiplication exponent ω<2.3727 is obtained.
Matrix Multiplication, a Little Faster
- Computer ScienceSPAA
- 2017
A generalization of Probert's lower bound that holds under change of basis is proved, showing that for matrix multiplication algorithms with a 2x2 base case, the leading coefficient of the algorithm cannot be further reduced, hence optimal.
Matrix Multiplication, a Little Faster
- Computer ScienceJ. ACM
- 2020
It is proved that for matrix multiplication algorithms with a 2 × 2 base case, the leading coefficient of Strassen-Winograd’s O(nlog27) algorithm cannot be further reduced, and is therefore optimal, and applied to other fast matrix multiplicationgorithms, improving their arithmetic and communication costs by significant constant factors.
Complexity Of Computations
- Mathematics, Computer ScienceACM Annual Conference
- 1978
Construction of algorithms is a time honored mathematical activity, with the whole field of Numerical Analysis devoted to finding a variety of algorithms for numerical integration of differential equations.
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