Bounds for Eigenvalues of Arrowhead Matrices and Their Applications to Hub Matrices and Wireless Communications. (13th December 2009)

• Record Type: Journal Article
• Authors: Shen, Lixin; Suter, Bruce W.
• Other Names: Capobianco Enrico Academic Editor.
• Is Part Of: EURASIP journal on advances in signal processing. Volume 2009(2009)
• Publication Date: 2009-12-13
• Subjects: Signal processing -- Periodicals; Traitement du signal; Signal processing; Periodicals; 621.3822
• DOI: 10.1155/2009/379402
• Languages: English
• ISSNs: 1687-6172

Abstract

Abstract : This paper considers the lower and upper bounds of eigenvalues of arrow-head matrices. We propose a parameterized decomposition of an arrowhead matrix which is a sum of a diagonal matrix and a special kind of arrowhead matrix whose eigenvalues can be computed explicitly. The eigenvalues of the arrowhead matrix are then estimated in terms of eigenvalues of the diagonal matrix and the special arrowhead matrix by using Weyl's theorem. Improved bounds of the eigenvalues are obtained by choosing a decomposition of the arrowhead matrix which can provide best bounds. Some applications of these results to hub matrices and wireless communications are discussed.