A New Fast Recursive Matrix Multiplication Algorithm

A new recursive algorithm is proposed for multiplying matrices of order n = 2 q ( q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4 μ with μ = 2 q −1 ( q > 0). As compared with the well-known recursive Strassen’s and Winograd–Strassen’s algorith...

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Vydané v:Cybernetics and systems analysis Ročník 55; číslo 4; s. 547 - 551
Hlavný autor: Jelfimova, L. D.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.07.2019
Springer
Springer Nature B.V
Predmet:
Algebra
Algorithms
Artificial Intelligence
Complexity
Control
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Multiplication
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
family of fast hybrid matrix multiplication algorithms
block-recursive Strassen’s algorithm
linear algebra
block-recursive Winograd’s–Strassen’s algorithm
ISSN:1060-0396, 1573-8337
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Abstract A new recursive algorithm is proposed for multiplying matrices of order n = 2 q ( q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4 μ with μ = 2 q −1 ( q > 0). As compared with the well-known recursive Strassen’s and Winograd–Strassen’s algorithms, the new algorithm minimizes the multiplicative complexity equal to W m ≈ 0.932 n 2.807 multiplication operations at recursive level d = log 2 n −3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated.
AbstractList A new recursive algorithm is proposed for multiplying matrices of order n = 2 q ( q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4 μ with μ = 2 q −1 ( q > 0). As compared with the well-known recursive Strassen’s and Winograd–Strassen’s algorithms, the new algorithm minimizes the multiplicative complexity equal to W m ≈ 0.932 n 2.807 multiplication operations at recursive level d = log 2 n −3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated.
A new recursive algorithm is proposed for multiplying matrices of order n = [2.sup.q] (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4[mu] with [mu] = [2.sup.q-1] (q > 0). As compared with the well-known recursive Strassen's and Winograd-Strassen's algorithms, the new algorithm minimizes the multiplicative complexity equal to [W.sub.m] [approximately equal to] 0.932[n.sup.2.807] multiplication operations at recursive level d = [log.sub.2] n - 3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated. Keywords: linear algebra, block-recursive Strassen's algorithm, block-recursive Winograd's-Strassen's algorithm, family of fast hybrid matrix multiplication algorithms.
A new recursive algorithm is proposed for multiplying matrices of order n = 2q (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4μ with μ = 2q−1 (q > 0). As compared with the well-known recursive Strassen’s and Winograd–Strassen’s algorithms, the new algorithm minimizes the multiplicative complexity equal to Wm ≈ 0.932n2.807 multiplication operations at recursive level d = log2n−3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated.
A new recursive algorithm is proposed for multiplying matrices of order n = [2.sup.q] (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying matrices of order n = 4[mu] with [mu] = [2.sup.q-1] (q > 0). As compared with the well-known recursive Strassen's and Winograd-Strassen's algorithms, the new algorithm minimizes the multiplicative complexity equal to [W.sub.m] [approximately equal to] 0.932[n.sup.2.807] multiplication operations at recursive level d = [log.sub.2] n - 3 by 7% and reduces the computation vector by three recursion steps. The multiplicative complexity of the algorithm is estimated.
Audience Academic
Author Jelfimova, L. D.
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Cites_doi 10.1109/TC.1968.227420
10.1023/A:1016676318988
10.1007/s10559-010-9233-y
10.1007/s10559-011-9367-6
10.1016/0024-3795(71)90009-7
10.1007/BF02165411
10.1090/S0002-9904-1976-13988-2
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Keywords family of fast hybrid matrix multiplication algorithms
block-recursive Strassen’s algorithm
linear algebra
block-recursive Winograd’s–Strassen’s algorithm
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Jelfimova (CR7) 2011; 47
Strassen (CR2) 1969; 13
JD Laderman (163_CR4) 1976; 82
V Strassen (163_CR2) 1969; 13
LD Jelfimova (163_CR6) 2010; 46
LD Jelfimova (163_CR7) 2011; 47
SA Winograd (163_CR1) 1968; C-18
S Winograd (163_CR3) 1971; 4
LD Elfimova (163_CR5) 2001; 37
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Snippet A new recursive algorithm is proposed for multiplying matrices of order n = 2 q ( q > 1). This algorithm is based on a fast hybrid algorithm for multiplying...
A new recursive algorithm is proposed for multiplying matrices of order n = [2.sup.q] (q > 1). This algorithm is based on a fast hybrid algorithm for...
A new recursive algorithm is proposed for multiplying matrices of order n = 2q (q > 1). This algorithm is based on a fast hybrid algorithm for multiplying...
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SubjectTerms Algebra
Algorithms
Artificial Intelligence
Complexity
Control
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Multiplication
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
Title A New Fast Recursive Matrix Multiplication Algorithm
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