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

作者：Gower JC^*

来源：Computational Statistics & Data Analysis, 2006, 50(1): 89-106.

DOI：10.1016/j.csda.2004.07.009

• algebraic algorithms
• Leverrier
• Faddeev
• block-circulants
• spectral decomposition
• singular value decomposition

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.

• 出版日期2006-1-10