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W publikacji przedstawiono zastosowanie teorii Perrona-Frobeniusa w spektralnej teorii rankingów.
Wydawca
Czasopismo
Rocznik
Tom
Strony
155--175
Opis fizyczny
Bibliogr. 33 poz., fot., rys.
Twórcy
Bibliografia
- [1] A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia 1994.
- [2] K. C. Chang, A nonlinear Krein-Rutman theorem, J. Syst. Sci. Complex 22 (2009), 542-554.
- [3] Y. Du, Order structure and topological methods in nonlinear partial differential equations, World Scientific, New Jersey 2006.
- [4] G. Frobenius, Über Matrizen aus positiven Elementen, S.-B. Preuss. Akad. Wiss. (1908), 471-476.
- [5] F. G. Frobenius, Über Matrizen aus nicht negativen Elementen, S.-B Preuss. Akad. Wiss. 26 (1912), 456-477.
- [6] F. R. Gantmacher, The Theory of Matrices, Volume I, II, Chelsea Publ. Co., New York 1959.
- [7] E. Garfield, The Agony and the Ecstasy – The History and Meaning of the Journal Impact Factor, Internat. Congress on Peer Review and Biomedical Publication (Chicago, 2008), dostępne pod adresem http://garfield.library.upenn.edu/papers/jifchicago2005.pdf.
- [8] T. Haveliwala, G. Jeh, S. Kamvar, An Analytical Comparison of Approaches to Personalizing PageRank, Stanford University Technical Report 2003.
- [9] T. Hawkins, Continued fractions and the origins of the Perron-Frobenius theorem, Arch. Hist. Exact Sci. 62 (2008), 655-717.
- [10] L. Katz, A new status index derived from sociometric analysis, Psychometrika 18 (1953), 39-43.
- [11] J. Keener, The Perron-Frobenius Theorem and the ranking of football teams, SIAM Rev. 35 (1993), 80-93.
- [12] M. G. Kendall, Further contributions to the theory of paired comparisons, Biometrics 11 (1955), 43-62.
- [13] S. Kirkland, P. Qiao, X. Zhan, Algebraically positive matrices, Lin. Algebra App. 1 (2016), 14-26.
- [14] E. Kohlberg, J. Pratt, The contraction mapping approach to the Perron-Frobenius theory: why Hilbert’s metric?, Math. Oper. Res. 7 (1982), 198-210.
- [15] A. N. Langville, C. D. Meyer, Google’s PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton 2006.
- [16] B. Lemmens, R. Nussbaum, Nonlinear Perron-Frobenius Theory, Cambridge Univ. Press, Cambridge 2012.
- [17] B. Liu, H.-J. Lai, Matrices in Combinatorics and Graph theory, Kluwer, Boston 2000.
- [18] C. R. MacCluer, The many proofs and applications of Perron’s theorem, SIAM Rev. 42 (2000), 487-498.
- [19] M. Marchiori, The quest for correct information on theWeb: hyper search engines, Comp. Networks ISDN Systems 29 (1997), 1225-1235.
- [20] C. Meyer, Matrix Algebra and Applied Linear Algebra, SIAM, Philadelphia 2004.
- [21] L. Page, S. Brin, R. Motwani, T. Winograd, The PageRank citation ranking: Bringing order to the web, Technical Report SIDL-WP-1999-0120, Stanford University 1998.
- [22] O. Perron, Grundlagen für eine Theorie des Jacobischen Kettenbrauchalgorithmus, Math. Ann. 63 (1907), 1-76.
- [23] O. Perron, Zur Theorie der Matrices, Math. Ann. 63 (1907), 248-263.
- [24] G. Pinski, F. Narin, Citation influence for journal aggregates of scientific publications: Theory, with application to the literature of physics, Inf. Process. Manage 12 (1976), 297-312.
- [25] T. L. Saaty, The analytical hierarchy process, McGraw-Hill, New York 1980.
- [26] T. L. Saaty, Rank according to Perron: A new insight, Math. Magazine 60 (1987), 211-213.
- [27] H. Scarf, The computation of equilibrium prices: an exposition, [w:] Handbook of Mathematical Economics (K. J. Arrow, M. D. Intriligator, red.), t. 11, North-Holland Publishing Company 1982, 1007-1061.
- [28] J. R. Seeley, The net of reciprocal influence: A problem in treating sociometric data, Canadian J. Psychology 3 (1949), 234-240.
- [29] B.-S. Tam, A cone-theoretic approach to the spectral theory of positive linear operators: The finite-dimensional case, Taiwanese J. Math. 207-277 (2001).
- [30] H. R. Thieme, Mathematics in Population Biology, Princeton Univ. Press, Princeton 2003.
- [31] S. Vigna, Spectral Ranking, Network Sci. 4 (2016), 433-445.
- [32] T.-H. Wei, The Algebraic Foundations of Ranking Theory, PhD Thesis, University of Cambridge 1952.
- [33] H. Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z. 52 (1950), 642-648.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7b2eede2-15e9-4386-9572-ead46b656c81