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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Vydáno v:Cybernetics and systems analysis Ročník 55; číslo 4; s. 547 - 551
Hlavní autor: Jelfimova, L. D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2019
Springer
Springer Nature B.V
Témata:
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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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-019-00163-2