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}
}
  • V. Pan
  • Published 16 October 1978
  • Computer Science
  • 19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
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. 
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  • V. Pan
  • Computer Science
    20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
TLDR
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.
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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 ...
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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 coecient of the Strassen-Winograd algorithm cannot be further reduced, hence optimal.
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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
TLDR
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.
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  • S. Winograd
  • Mathematics, Computer Science
    ACM Annual Conference
  • 1978
TLDR
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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