On some aspects of spectral theory for infinite bounded non-negative matrices in max algebra

References

• Baccelli FL, Cohen G, Olsder G-J, et al. Synchronization and linearity. Chichester (NY): John Wiley; 1992.
   Google Scholar
• Bapat RB. A max version of the Perron–Frobenius theorem. Linear Algebra Appl. 1998;275–276:3–18.
   Web of Science ®Google Scholar
• Bapat RB, Stanford DP, van den Driessche P. Pattern properties and spectral inequalities in max algebra. SIAM J Matrix Anal Appl. 1995;16:964–976.
   Web of Science ®Google Scholar
• Butkovič P. Max-linear systems: theory and algorithms. London: Springer-Verlag; 2010.
   Google Scholar
• Gaubert S. Théorie des systemes linéaires dans les dioïdes [These]. Ecole des Mines de Paris; 1992.
   Google Scholar
• Guglielmi N, Mason O, Wirth F. Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius. Linear Algebra Appl. 2018;550:37–58. E-print: arXiv:1705.02008v1
   Web of Science ®Google Scholar
• Heidergott B, Olsder GJ, van der Woudel J. Max plus at work. 2006. (Princeton series in applied mathematics).
   Google Scholar
• Peperko A. On the continuity of the generalized spectral radius in max algebra. Linear Algebra Appl. 2011;435:902–907.
   Web of Science ®Google Scholar
• Khaleghzade S, Zangiabadi M, Peperko A, et al. Perron–Frobenius theory for some classes of nonnegative tensors in the max algebra. Linear Algebra Appl. 2022;641:115–142.
   Web of Science ®Google Scholar
• Elsner L, van den Driessche P. Bounds for the Perron root using max eigenvalues. Linear Algebra Appl. 2008;428:2000–2005.
   Web of Science ®Google Scholar
• Gabrovšek B, Peperko A, Žerovnik J. Independent rainbow domination numbers of generalized Petersen graphs P(n,2) and P(n,3). Mathematics. 2020;8:996. DOI:10.3390/math8060996
   Web of Science ®Google Scholar
• Müller V, Peperko A. Generalized spectral radius and its max algebra version. Linear Algebra Appl. 2013;439:1006–1016.
   Web of Science ®Google Scholar
• Akian M, Bapat R, Gaubert S. Perturbation of eigenvalues of matrix pencils and optimal assignment problem. C R Acad Sci Paris Serie I. 2004;339:103–108. E-print: arXiv:math.SP/0402438
   Google Scholar
• Akian M, Bapat R, Gaubert S. Min-plus methods in eigenvalue perturbation theory and generalised Lidskii–Vishik–Ljusternik theorem, 2005. E-print: arXiv:math.SP/0402090.
   Google Scholar
• Akian M, Gaubert S, Sharify M. Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots. Linear Algebra Appl. 2017;528:394–435. E-print: arxiv.org/abs/1304.2967
   Web of Science ®Google Scholar
• Bini DA, Noferini V, Sharify M. Locating the eigenvalues of matrix polynomials. SIAM J Matrix Anal Appl. 2013;34(4):1708–1727. E-print: arxiv.org/abs/1206.3632
   Web of Science ®Google Scholar
• Gaubert S, Sharify M. Tropical scaling of polynomial matrices. Lect Notes Control Inf Sci. 2009;389:291–303.
   Google Scholar
• Akian M, Gaubert S, Walsh C. Discrete max-plus spectral theory. In: Litvinov GL, Maslov VP, editors. Idempotent mathematics and mathematical physics. AMS; 2005. p. 53–77 (Contemporary mathematics; vol. 377). E-print: arXiv:math.SP/0405225.
   Google Scholar
• Butkovič P, Gaubert S, Cuninghame-Green RA. Reducible spectral theory with applications to the robustness of matrices in max-algebra. SIAM J Matrix Anal Appl. 2009;31(3):1412–1431.
   Web of Science ®Google Scholar
• Kolokoltsov VN, Maslov VP. Idempotent analysis and its applications. Boston (MA): Kluwer Acad. Publ.; 1997.
   Google Scholar
• Mallet-Paret J, Nussbaum RD. Eigenvalues for a class of homogeneous cone maps arising from max-plus operators. Discrete Continuous Dyn Syst. 2002;8(3):519–562.
   Web of Science ®Google Scholar
• Shpiz GB. An eigenvector existence theorem in idempotent analysis. Math Notes. 2007;82(3–4):410–417.
   Web of Science ®Google Scholar
• Appell J, De Pascale E, Vignoli A. Nonlinear spectral theory. Berlin (KG): Walter de Gruyter GmbH and Co; 2004.
   Google Scholar
• Lemmens B, Nussbaum RD. Continuity of the cone spectral radius. Proc AMS. 2013;141:2741–2754.
   Web of Science ®Google Scholar
• Litvinov GL, Maslov VP, editors. Idempotent mathematics and mathematical physics. Providence (RI): Amer. Math. Soc.; 2005 (Contemporary mathematics; vol. 377).
   Google Scholar
• Mallet-Paret J, Nussbaum RD. Generalizing the Krein–Rutman theorem, measures of noncompactness and the fixed point index. J Fixed Point Theory Appl. 2010;7:103–143.
   Web of Science ®Google Scholar
• Müller V, Peperko A. On the Bonsall cone spectral radius and the approximate point spectrum. Discrete Continuous Dyn Syst Ser A. 2017;37(10):5337–5364.
   Web of Science ®Google Scholar
• Müller V, Peperko A. Lower spectral radius and spectral mapping theorem for suprema preserving mappings. Discrete Continuous Dyn Syst Ser A. 2018;38(8):4117–4132.
   Web of Science ®Google Scholar
• Nussbaum RD. Eigenvalues of nonlinear operators and the linear Krein–Rutman. In: Fadell E, Fournier G, editors. Fixed point theory (Sherbrooke, Quebec, 1980). Berlin: Springer-Verlag; 1981. p. 309–331 (Lecture notes in mathematics; 886).
   Google Scholar
• Nussbaum RD. Convexity and log convexity for the spectral radius. Linear Algebra Appl. 1986;73:59–122.
   Web of Science ®Google Scholar
• Katz RD, Schneider H, Sergeev S. On commuting matrices in max algebra and in nonnegative matrix algebra. Linear Algebra Appl. 2012;436(2):276–292.
   Web of Science ®Google Scholar
• Elsner L, Johnson CR, Dias Da Silva JA. The Perron root of a weighted geometric mean of nonnegative matrices. Linear Multilinear Algebra. 1988;24:1–13.
   Google Scholar
• Peperko A. Inequalities for the spectral radius of non-negative functions. Positivity. 2009;13:255–272.
   Web of Science ®Google Scholar
• Peperko A. On the max version of the generalized spectral radius theorem. Linear Algebra Appl. 2008;428:2312–2318.
   Web of Science ®Google Scholar
• Bapat RB, Stanford DP, van den Driessche P. The eigenproblem in max algebra, DMS-631-IR. University of Victoria, Victoria, BC, 1993.
   Google Scholar
• Bapat RB, Raghavan TES. Nonnegative matrices and applications. Cambridge: Cambridge University Press; 1997.
   Google Scholar
• Butkovič P, Schneider H, Sergeev S, et al. Two cores of a non-negative matrix. Linear Algebra Appl. 2013;439:1929–1954.
   Web of Science ®Google Scholar
• Gunawardena J. Cycle times and fixed points of min–max functions. In: Cohen G, Quadrat J-P, editors. 11th International conference on analysis and optimization of systems. 1994. p. 266–272 (Springer LNCIS; 199).
   Google Scholar
• Müller V, Peperko A. On the spectrum in max algebra. Linear Algebra Appl. 2015;485:250–266.
   Web of Science ®Google Scholar