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

  • Otto Lange
Architectural Aspects (Session 5.1)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)


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.


Kronecker Product Orthogonal Transformation Spectral Coefficient Processor Element Processor Network 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Otto Lange
    • 1
  1. 1.Allgemeine Elektrotechnik und DatenverarbeitungssystemeRWTH AachenGermany

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