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: https://doi.org/10.1016/j.csda.2004.07.009

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.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 2747
• Item Type
• Journal Item
• 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 or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Heather Whitaker