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Sib. Zh. Vychisl. Mat., 2017, Volume 20, Number 4, Pages 359–378 (Mi sjvm657)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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


DOI: https://doi.org/10.15372/SJNM20170402

Full text: PDF file (4673 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Numerical Analysis and Applications, 2017, 10:4, 299–312

Bibliographic databases:

UDC: 519.217.2+519.614.2
Received: 07.03.2017
Revised: 15.05.2017

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
\Bibitem{GasGasDvu17}
\by A.~Gasnikov, E.~Gasnikova, P.~Dvurechensky, A.~Mohammed, E.~Chernousova
\paper About the power law of the PageRank vector distribution. Part~1. Numerical methods for finding the PageRank vector
\jour Sib. Zh. Vychisl. Mat.
\yr 2017
\vol 20
\issue 4
\pages 359--378
\mathnet{http://mi.mathnet.ru/sjvm657}
\crossref{https://doi.org/10.15372/SJNM20170402}
\elib{http://elibrary.ru/item.asp?id=30564535}
\transl
\jour Num. Anal. Appl.
\yr 2017
\vol 10
\issue 4
\pages 299--312
\crossref{https://doi.org/10.1134/S1995423917040024}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042731035}


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    This publication is cited in the following articles:
    1. 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
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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