article

Kronecker products and shuffle algebra

Author:

Marc DavioAuthors Info & Claims

IEEE Transactions on Computers, Volume 30, Issue 2

Pages 116 - 125

Published: 01 February 1981 Publication History

Abstract

The paper relates three classical concepts, viz. mixed radix number system, Kronecker product of matrices, and perfect shuffle. It presents an algebra which describes the hardware organization of the computation of a product Mv, where M is a matrix in Kronecker product form and v is a vector. The algebraic formalism describes both the blockwise structure of the computation and the various possible connection patterns.

References

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Cited By

Fackler P(2019)Algorithm 993ACM Transactions on Mathematical Software10.1145/329104145:2(1-9)Online publication date: 3-May-2019
https://dl.acm.org/doi/10.1145/3291041
(2017)Shuffling matrices, Kronecker product and Discrete Fourier TransformDiscrete Applied Mathematics10.1016/j.dam.2017.08.018233:C(1-18)Online publication date: 31-Dec-2017
https://dl.acm.org/doi/10.1016/j.dam.2017.08.018
Mittermayr RBlieberger J(2016)Kronecker Algebra for Static Analysis of Barriers in AdaProceedings of the 21st Ada-Europe International Conference on Reliable Software Technologies --- Ada-Europe 2016 - Volume 969510.1007/978-3-319-39083-3_10(145-159)Online publication date: 13-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-39083-3_10
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Published In

cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 30, Issue 2

February 1981

85 pages

ISSN:0018-9340

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IEEE Computer Society

United States

Publication History

Published: 01 February 1981

Revised: 10 March 1980

Received: 02 April 1979

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Cited By

Fackler P(2019)Algorithm 993ACM Transactions on Mathematical Software10.1145/329104145:2(1-9)Online publication date: 3-May-2019
https://dl.acm.org/doi/10.1145/3291041
(2017)Shuffling matrices, Kronecker product and Discrete Fourier TransformDiscrete Applied Mathematics10.1016/j.dam.2017.08.018233:C(1-18)Online publication date: 31-Dec-2017
https://dl.acm.org/doi/10.1016/j.dam.2017.08.018
Mittermayr RBlieberger J(2016)Kronecker Algebra for Static Analysis of Barriers in AdaProceedings of the 21st Ada-Europe International Conference on Reliable Software Technologies --- Ada-Europe 2016 - Volume 969510.1007/978-3-319-39083-3_10(145-159)Online publication date: 13-Jun-2016
https://dl.acm.org/doi/10.1007/978-3-319-39083-3_10
Gao LCalo V(2015)Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficientsJournal of Computational and Applied Mathematics10.1016/j.cam.2014.06.021273:C(274-295)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.cam.2014.06.021
Czekster RFernandes PWebber T(2011)Efficient vector-descriptor product exploiting time-memory trade-offsACM SIGMETRICS Performance Evaluation Review10.1145/2160803.216080539:3(2-9)Online publication date: 21-Dec-2011
https://dl.acm.org/doi/10.1145/2160803.2160805
Czekster RDe Rose CFernandes Pde Lima AWebber TMcGraw RImsand EChinni M(2010)Kronecker descriptor partitioning for parallel algorithmsProceedings of the 2010 Spring Simulation Multiconference10.1145/1878537.1878789(1-4)Online publication date: 11-Apr-2010
https://dl.acm.org/doi/10.1145/1878537.1878789
Czekster RFernandes PVincent JWebber TGlynn P(2007)SplitProceedings of the 2nd international conference on Performance evaluation methodologies and tools10.5555/1345263.1345372(1-8)Online publication date: 22-Oct-2007
https://dl.acm.org/doi/10.5555/1345263.1345372
Järvinen TSalmela PSorokin HTakala J(2007)Stride Permutation Networks for Array ProcessorsJournal of VLSI Signal Processing Systems10.1007/s11265-006-0031-849:1(51-71)Online publication date: 1-Oct-2007
https://dl.acm.org/doi/10.1007/s11265-006-0031-8
Miner A(2006)Saturation for a General Class of ModelsIEEE Transactions on Software Engineering10.1109/TSE.2006.8132:8(559-570)Online publication date: 1-Aug-2006
https://dl.acm.org/doi/10.1109/TSE.2006.81
Nikara JTakala JAstola J(2006)Discrete cosine and sine transformsSignal Processing10.1016/j.sigpro.2005.05.01486:2(230-249)Online publication date: 1-Feb-2006
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