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Fast matrix multiplication

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Charles M. FiducciaAuthors Info & Claims

STOC '71: Proceedings of the third annual ACM symposium on Theory of computing

Pages 45 - 49

https://doi.org/10.1145/800157.805037

Published: 03 May 1971 Publication History

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Abstract

This paper deals with three aspects of algebraic complexity. The first section is concerned with lower bounds on the number of operations required to compute several functions. Several theorems are presented and their proofs sketched. The second section deals with relationships among the complexities of several sets of functions. In the third section, several matrices of general interest are examined and upper bounds on the number of operations required to multiply by them are constructively derived.

References

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Ostrowski, A.M., "On two problems in abstract algebra connected with Horner's rule," Studies presented to R. vonMises, Academic Press, New York, 1954, pp. 40-48.

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Winograd, S., "On the number of multiplications necessary to compute certain functions," Comm. Pure and Applied Math, vol. 23, 1970, pp. 165-179.

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Winograd, S., "On the multiplication of 2×2 matrices," IBM Research Report RC267, Jan. 1970.

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Cooley, J.W. and J.W. Tuckey, "An algorithm for the machine computation of complex Fourier series," Math. Computation, vol.19, April 1965, pp. 297-301.

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Rader, C.M., "Discrete Fourier transforms when the number of data samples is prime," Proc. IEEE, vol. 56, June 1968, pp. 1107-1108.

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Fiduccia, C.M., "Fast matrix multiplication," Doctoral dissertation (being completed), Brown University.

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Cited By

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Dumas JPernet CSedoglavic A(2023)Some fast algorithms multiplying a matrix by its adjointJournal of Symbolic Computation10.1016/j.jsc.2022.08.009115:C(285-315)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jsc.2022.08.009
Probert R(2016) On The Complexity Of Symmetric Computations * INFOR: Information Systems and Operational Research10.1080/03155986.1974.1173156512:1(71-86)Online publication date: 25-May-2016
https://doi.org/10.1080/03155986.1974.11731565
Bini DPan V(2005)Algorithms for polynomial divisionEUROCAL '8510.1007/3-540-15984-3_229(1-3)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-15984-3_229
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Index Terms

Fast matrix multiplication
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computation of transforms
      2. Computations on matrices

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Fast Rectangular Matrix Multiplication and Applications

First we study asymptotically fast algorithms for rectangular matrix multiplication. We begin with new algorithms for multiplication of ann nmatrix by ann n2matrix in arithmetic timeO(n ), =3.333953 , which is less by 0.041 than the previous record ...
Fast rectangular matrix multiplication (algebraic computational, asymptotic complexity)

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STOC '71: Proceedings of the third annual ACM symposium on Theory of computing

May 1971

270 pages

ISBN:9781450374644

DOI:10.1145/800157

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 03 May 1971

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STOC '71 Paper Acceptance Rate 23 of 50 submissions, 46%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Dumas JPernet CSedoglavic A(2023)Some fast algorithms multiplying a matrix by its adjointJournal of Symbolic Computation10.1016/j.jsc.2022.08.009115:C(285-315)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1016/j.jsc.2022.08.009
Probert R(2016) On The Complexity Of Symmetric Computations * INFOR: Information Systems and Operational Research10.1080/03155986.1974.1173156512:1(71-86)Online publication date: 25-May-2016
https://doi.org/10.1080/03155986.1974.11731565
Bini DPan V(2005)Algorithms for polynomial divisionEUROCAL '8510.1007/3-540-15984-3_229(1-3)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-15984-3_229
Kreczmar A(2005)On memory requirements of Strassen's algorithmsMathematical Foundations of Computer Science 197610.1007/3-540-07854-1_206(404-407)Online publication date: 21-May-2005
https://doi.org/10.1007/3-540-07854-1_206
Bevilacqua RBozzo ETemperanza GZellini P(1993)Complexity bounds for solving some tridiagonal systems with preconditioningCalcolo10.1007/BF0257617730:2(127-143)Online publication date: Jun-1993
https://doi.org/10.1007/BF02576177
Bshouty N(1989)On the extended direct sum conjectureProceedings of the twenty-first annual ACM symposium on Theory of computing10.1145/73007.73024(177-185)Online publication date: 1-Feb-1989
https://dl.acm.org/doi/10.1145/73007.73024
Morgera SKrishna H(1989)Systems of Bilinear FormsDigital Signal Processing10.1016/B978-0-12-506995-3.50009-6(11-27)Online publication date: 1989
https://doi.org/10.1016/B978-0-12-506995-3.50009-6
Pan V(1982)Trilinear aggregating with implicit canceling for a new acceleration of matrix multiplicationComputers & Mathematics with Applications10.1016/0898-1221(82)90037-28:1(23-34)Online publication date: 1982
https://doi.org/10.1016/0898-1221(82)90037-2
Makarov O(1981)Dual problems of multiplication of a vector by a matrixMathematical Notes of the Academy of Sciences of the USSR10.1007/BF0114021230:5(817-821)Online publication date: Nov-1981
https://doi.org/10.1007/BF01140212
Ja'Ja' JFischer MDemillo RLynch NBurkhard WAho A(1979)On the complexity of bilinear forms with commutativityProceedings of the eleventh annual ACM symposium on Theory of computing10.1145/800135.804413(197-208)Online publication date: 30-Apr-1979
https://dl.acm.org/doi/10.1145/800135.804413
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Powers of tensors and fast matrix multiplication

Fast Rectangular Matrix Multiplication and Applications

Fast rectangular matrix multiplication (algebraic computational, asymptotic complexity)

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Powers of tensors and fast matrix multiplication

Fast Rectangular Matrix Multiplication and Applications

Fast rectangular matrix multiplication (algebraic computational, asymptotic complexity)

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