publication . Preprint . 2013

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David;
Open Access English
  • Published: 27 Aug 2013
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 matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the PF Theorem (along with its applications) can be generalized to a nonsquare setting. Our paper provides a generalization of the PF Theorem to nonsquare matrices. The extensi...
free text keywords: Computer Science - Numerical Analysis
Download from
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. [OpenAIRE]

[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. [OpenAIRE]

[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.

[22] V. Mehrmann, R. Nabben, and E. Virnik. On Perron-Frobenius property of matrices having some negative entries. Lin. Algeb. & its Applic., 412:132{153, 2006.

[23] C. W. Sung. Log-convexity property of the feasible SIR region in power-controlled cellular systems. IEEE Comm. Lett., 6:209{212, 2002.

[25] K. Pahlavan and A. Levesque. Wireless information networks. Wiley, 1995.

[26] O. Perron. Grundlagen fur eine theorie des Jacobischen kettenbruchalgorithmus. Mathematische Annalen, 64:248{263, 1907. [OpenAIRE]

[27] S.U. Pillai, T. Suel, and S. Cha. The Perron-Frobenius theorem. IEEE Signal Process. Mag., 22:62{75, 2005. [OpenAIRE]

18 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue