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An application of the modified Leverrier–Faddeev algorithm to the spectral decomposition of symmetric block-circulant matrices

Gower, John C. (2006). An application of the modified Leverrier–Faddeev algorithm to the spectral decomposition of symmetric block-circulant matrices. Computational Statistics and Data Analysis, 50(1) pp. 89–106.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1016/j.csda.2004.07.009
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Abstract

The Leverrier–Faddeev algorithm is little-known but, in a modified form, is useful for deriving the algebraic, rather than numerical, spectral structure of matrices occurring in statistical methodology. An example is given of deriving the spectral decomposition of any symmetric block-circulant matrix, which in turn provides the singular value decomposition of any block-circulant matrix. Such problems arise as short-cuts to certain computations that arise in special forms of principal components analysis and correspondence analysis.

Item Type: Journal Article
ISSN: 0167-9473
Extra Information: 2nd Special issue on Matrix Computations and Statistics
Keywords: Algebraic algorithms; Leverrier; Faddeev; Block-circulants; Spectral decomposition; Singular value decomposition
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 2747
Depositing User: Heather Whitaker
Date Deposited: 29 Jun 2006
Last Modified: 02 Dec 2010 19:48
URI: http://oro.open.ac.uk/id/eprint/2747
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