Twierdzenie Perrona-Frobeniusa, Google i tenis

• Autorzy: Kryszewski W.
• Języki publikacji: PL

Abstrakty

PL

W publikacji przedstawiono zastosowanie teorii Perrona-Frobeniusa w spektralnej teorii rankingów.

Słowa kluczowe

PL

teoria Perrona-Frobeniusa; ranking spektralny; ranking sportowy; wzór Collatza-Wielandta; algorytm PageRank; Google; strona internetowa; teoria spektralna macierzy

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2018
• Tom: T. 54, Nr 2
• Strony: 155--175
• Opis fizyczny: Bibliogr. 33 poz., fot., rys.

Twórcy

autor

Kryszewski W.

• Politechnika Łódzka, Łódź, Polska

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.