Shen, Lixin; Suter, Bruce W. Bounds for eigenvalues of arrowhead matrices and their applications to hub matrices and wireless communications. (English) Zbl 1192.15018 EURASIP J. Adv. Signal Process. 2009, Article ID 379402, 12 p. (2009). Summary: 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. Cited in 2 Documents MSC: 15B99 Special matrices 90B18 Communication networks in operations research 94A12 Signal theory (characterization, reconstruction, filtering, etc.) PDFBibTeX XMLCite \textit{L. Shen} and \textit{B. W. Suter}, EURASIP J. Adv. Signal Process. 2009, Article ID 379402, 12 p. (2009; Zbl 1192.15018) Full Text: DOI References: [2] doi:10.1103/PhysRevB.24.1651 [5] doi:10.1088/0266-5611/3/4/010 · Zbl 0633.65036 [6] doi:10.1016/j.laa.2007.10.040 · Zbl 1141.15010 [7] doi:10.1016/j.laa.2005.11.017 · Zbl 1097.65053 [8] doi:10.1016/j.laa.2007.07.020 · Zbl 1144.65026 [9] doi:10.1155/2007/13659 · Zbl 1168.90370 [15] doi:10.1016/0024-3795(80)90258-X · Zbl 0435.15015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.