báo cáo hóa học:" Research Article Bounds for Eigenvalues of Arrowhead Matrices and Their Applications to Hub Matrices and Wireless Communications"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Bounds for Eigenvalues of Arrowhead Matrices and Their Applications to Hub Matrices and Wireless Communications | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2009 Article ID 379402 12 pages doi 2009 379402 Research Article Bounds for Eigenvalues of Arrowhead Matrices and Their Applications to Hub Matrices and Wireless Communications Lixin Shen1 and Bruce W. Suter2 1 Department of Mathematics Syracuse University Syracuse NY 13244 USA 2 Air Force Research Laboratory RITC Rome NY 13441-4505 USA Correspondence should be addressed to Bruce W. Suter Received 29 June 2009 Accepted 15 September 2009 Recommended by Enrico Capobianco 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. Copyright 2009 L. Shen and B. W. Suter. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In this paper we develop lower and upper bounds for arrowhead matrices. A matrix Q e Rmxm is called an arrowhead matrix if it has a form as follows D c Q c b 1 where D e R m-1 x m-1 is a diagonal matrix c is a vector in Rm and b is a real number. Here the superscript signifies the transpose. The arrowhead matrix Q is obtained by bordering the diagonal matrix D by the vector c and the real number b. Hence sometimes the matrix Q in 1 is also called a symmetric bordered diagonal

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