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Title: Computation of the canonical decomposition by means of a simultaneous generalized Schur decomposition
Authors: De Lathauwer, Lieven ×
De Moor, Bart
Vandewalle, Joos #
Issue Date: 2004
Publisher: Society for Industrial and Applied Mathematics
Series Title: SIAM Journal on Matrix Analysis and Applications vol:26 issue:2 pages:295-327
Abstract: The canonical decomposition of higher-order tensors is a key tool in multilinear algebra. First we review the state of the art. Then we show that, under certain conditions, the problem can be rephrased as the simultaneous diagonalization, by equivalence or congruence, of a set of matrices. Necessary and sufficient conditions for the uniqueness of these simultaneous matrix decompositions are derived. In a next step, the problem can be translated into a simultaneous generalized Schur decomposition, with orthogonal unknowns [A.-J. van der Veen and A. Paulraj, IEEE Trans. Signal Process., 44 (1996), pp. 1136-1155]. A first-order perturbation analysis of the simultaneous generalized Schur decomposition is carried out. We discuss some computational techniques (including a new Jacobi algorithm) and illustrate their behavior by means of a number of numerical experiments.
URI: 
ISSN: 0895-4798
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
Faculty of Science, Campus Kulak Kortrijk
× corresponding author
# (joint) last author

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