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International Conference on Parallel Processing

CONPAR 1986: CONPAR 86 pp 353–360Cite as

Kronecker products of matrices and their implementation on shuffle/exchange-type processor networks

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 237))

Abstract

In generalized spectral analysis an orthogonal transformation provides a set of spectral coefficients by a vector-matrix-multiplication. If the pnxpn-transformation matrix Hn is a Kronecker product of n pxp-matrices Mr, r=0,1,...,n−1, then — as has been shown by Good — there exists a factorization \(\mathop \prod \limits_{r = 0}^{n - 1} \)Gr of the transformation matrix Hn in such a way that the vector-matrix-multiplication can be reduced from 0(N2) to 0(NlogN) operations, where N=pn. The specific structure of the matrix factors Gr, r=0,1...,n−1, permits an implementation of the multiplication on processor networks, in case of p=2 on permutation networks of the Shuffle/Exchange-type.

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References

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Authors and Affiliations

  1. Allgemeine Elektrotechnik und Datenverarbeitungssysteme, RWTH Aachen, Germany

    Otto Lange

Authors
  1. Otto Lange
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Wolfgang Händler Dieter Haupt Rolf Jeltsch Wilfried Juling Otto Lange

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© 1986 Springer-Verlag Berlin Heidelberg

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Lange, O. (1986). Kronecker products of matrices and their implementation on shuffle/exchange-type processor networks. In: Händler, W., Haupt, D., Jeltsch, R., Juling, W., Lange, O. (eds) CONPAR 86. CONPAR 1986. Lecture Notes in Computer Science, vol 237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16811-7_190

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  • DOI: https://doi.org/10.1007/3-540-16811-7_190

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16811-9

  • Online ISBN: 978-3-540-44856-3

  • eBook Packages: Springer Book Archive

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