Generalized Perron--Frobenius Theorem for Nonsquare Matrices

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Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David;
(2013)
  • Subject: Computer Science - Numerical Analysis

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrice... View more
  • References (18)
    18 references, page 1 of 2

    1(A) 0 Algorithm ComputeP(L) /* Binary search phase: nding 1. 1; 2. While f ( ; L) = 1 do: 2 ; 3. If > 1, then =2, else 4. + ; 5. While + do:

    [1] C. Avin, A. Cohen, Y. Haddad, E. Kantor, Z. Lotker, M. Parter, and D. Peleg. SINR diagram with interference cancellation. In Proc. 23rd ACM-SIAM SODA, 502{515, 2012.

    [2] C. Avin, Y. Emek, E. Kantor, Z. Lotker, D. Peleg, and L. Roditty. SINR Diagrams: Convexity and Its Applications in Wireless Networks J. ACM, 59(4): 18, 2012.

    [3] U. Black. Mobile and Wireless Networks. Prentice Hall, 1996.

    [5] S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge Univ. Press, NY, 2004.

    [6] Y. Bugeaud and M. Mignotte. On the distance between roots of integer polynomials. In Proc. Edinburgh Math. Soc., vol. 47, 553{556. Cambridge Univ. Press, 2004.

    [7] D. W. H. Cai, T. Q. S. Quek, and C. W. Tan. A uni ed analysis of max-min weighted SINR for MIMO downlink system. IEEE Tr. Signal Process., 59, 2011.

    [8] D. W. H. Cai, T. Q. S. Quek, C. W. Tan, and S. H. Low. Max-min weighted SINR in coordinated multicell MIMO downlink. In Proc. WiOpt, 2011.

    [9] M. Chiang, P. Hande, T. Lan, and C. W. Tan. Power control in wireless cellular networks. Foundations and Trends in Networking, 2(4):381{533, 2007.

    [21] O.L. Mangasarian. Perron-Frobenius properties of Ax = 36, 1971.

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