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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 4, Pages 359–378
DOI: https://doi.org/10.15372/SJNM20170402 (Mi sjvm657) 		 
This article is cited in 6 scientific papers (total in 6 papers)

About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector

A. Gasnikovab, E. Gasnikovaa, P. Dvurechenskybc, A. Mohammeda, E. Chernousovaa

a Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, 141700, Russia
b Institute for Information Transmission Problems RAS, 19, build. 1, Bolshoy Karetny per., Moscow, 127051, Russia
c Weierstrass Institute for Applied Analysis and Stochastics, 39 Mohrenstr., Berlin, 10117, Germany
Full-text PDF (4673 kB) Citations (6)
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DOI: https://doi.org/10.15372/SJNM20170402
Abstract: In Part 1 of this paper, we consider the web-pages ranking problem also known as the problem of finding the PageRank vector or Google problem. We discuss the connection of this problem with the ergodic theorem and describe different numerical methods to solve this problem together with their theoretical background, such as Markov Chain Monte Carlo and equilibrium in a macrosystem.
Key words: Markov chain, ergodic theorem, multinomial distribution, measure concentration, maximum likelihood estimate, Google problem, gradient descent, automatic differentiation, power law distribution.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-1806.2017.9
Russian Science Foundation 14-50-00150
Received: 07.03.2017
Revised: 15.05.2017
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 4, Pages 299–312
DOI: https://doi.org/10.1134/S1995423917040024
Bibliographic databases:
Document Type: Article
UDC: 519.217.2+519.614.2
Language: Russian
Citation: A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, “About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 359–378; Num. Anal. Appl., 10:4 (2017), 299–312
Citation in format AMSBIB
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\pages 359--378
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  • https://www.mathnet.ru/eng/sjvm/v20/i4/p359
    Cycle of papers
    This publication is cited in the following 6 articles:
    1. Pavel Dvurechensky, Alexander Gasnikov, Alexander Tyurin, Vladimir Zholobov, Springer Proceedings in Mathematics & Statistics, 425, Foundations of Modern Statistics, 2023, 511  crossref
    2. P. Dvurechensky, E. Gorbunov, A. Gasnikov, “An accelerated directional derivative method for smooth stochastic convex optimization”, Eur. J. Oper. Res., 290:2 (2021), 601–621  crossref  mathscinet  isi  scopus
    3. Mikhail Koshelev, “New lower bound on the modularity of Johnson graphs”, Moscow J. Comb. Number Th., 10:1 (2021), 77  crossref
    4. Nikita Derevyanko, Mikhail Koshelev, Andrei Raigorodskii, Trends in Mathematics, 14, Extended Abstracts EuroComb 2021, 2021, 221  crossref
    5. K. Kovalenko, “On the independence number and the chromatic number of generalized preferential attachment models”, Discret Appl. Math., 285 (2020), 301–306  crossref  mathscinet  zmath  isi  scopus
    6. A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Num. Anal. Appl., 11:1 (2018), 16–32  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Sibirskii Zhurnal Vychislitel'noi Matematiki
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    References:53
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