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Bounds for eigenvalues of arrowhead matrices and their applications to hub matrices and wireless communications. (English) Zbl 1192.15018

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.

MSC:

15B99 Special matrices
90B18 Communication networks in operations research
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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References:

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