On the lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse M-matrix

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Özel M.

International Conference on Applied Analysis and Algebra, İstanbul, Turkey, 20 - 24 June 2012, pp.72-73

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.72-73
  • Dokuz Eylül University Affiliated: Yes

Abstract

Abstract: In this study, for the minimum eigenvalue 1()AAτ− of the Hadamard product 1AA− of an M-matrix A and its inverse1A− are considered. Some new lower bounds on 1()AAτ− for the Hadamard product of A and 1A− are derived. These bounds improve the results found in [H.B. Li, T.Z. Huang, S.Q. Shen, and H. Li. Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse. Linear Algebra Appl., 420:235-247, 2007] and [Y.T. Li, F.B. Chen, and D.F. Wang. New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse. Linear Algebra Appl., 430:1423-1431, 2009] and [Y.T. Li, X. Liu, X. Y. Yang, C. Q.Li. Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse. Electronic Journal of Linear Algebra, 22:630-643, 2011].

Keywords: Hadamard Product, M-Matrix, Minimum Eigenvalue, Lower Bounds.