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Jacobi Angles For Simultaneous Diagonalization. (1996)
| Venue: | SIAM J. Mat. Anal. Appl |
| Citations: | 192 - 3 self |
BibTeX
@ARTICLE{Cardoso96jacobiangles,
author = {Jean-François Cardoso and Jean-fran Cois Cardoso and ANTOINE SOULOUMIAC},
title = {Jacobi Angles For Simultaneous Diagonalization.},
journal = {SIAM J. Mat. Anal. Appl},
year = {1996},
volume = {17},
pages = {161--164}
}
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Abstract
. Simultaneous diagonalization of several matrices can be implemented by a Jacobi-like technique. This note gives the required Jacobi angles in close form. Key words. Simultaneous diagonalization, Jacobi iterations, eigenvalues, eigenvectors, structured eigenvalue problem. AMS subject classifications. 65F15, 65-04. Introduction. Simultaneous diagonalization of several commuting matrices has been recently considered in [1], mainly motivated by stability and convergence concerns. Exact or approximate simultaneous diagonalization was also independently introduced as a solution to a statistical identification problem [2] (see [3] for a later paper in English). The simultaneous diagonalization algorithm described in these papers is an extension of the Jacobi technique: a joint diagonality criterion is iteratively optimized under plane rotations. The purpose of this note is to complement [1] by giving a close form expression for the optimal Jacobi angles. 1. Jacobi angles in close form. C...
Keyphrases
simultaneous diagonalization jacobi angle close form jacobi-like technique statistical identification problem joint diagonality criterion am subject classification several matrix jacobi iteration convergence concern key word close form expression eigenvalue problem jacobi technique plane rotation later paper optimal jacobi angle simultaneous diagonalization algorithm required jacobi angle
