Taiwanese Journal of Mathematics

A Modified Newton Method for Multilinear PageRank

Pei-Chang Guo, Shi-Chen Gao, and Xiao-Xia Guo

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Abstract

When studying the multilinear PageRank problem, a system of polynomial equations needs to be solved. In this paper, we propose a modified Newton method and develop a monotone convergence theory for a third-order tensor when $\alpha \lt 1/2$. In this parameter regime, the sequence of vectors produced by the Newton-like method is monotonically increasing and converges to the solution. When $\alpha \gt 1/2$ we present an always-stochastic modified Newton iteration. Numerical results illustrate the effectiveness of this method.

Article information

Source
Taiwanese J. Math., Volume 22, Number 5 (2018), 1161-1171.

Dates
Received: 10 August 2017
Revised: 9 December 2017
Accepted: 15 March 2018
First available in Project Euclid: 23 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1521792084

Digital Object Identifier
doi:10.11650/tjm/180303

Mathematical Reviews number (MathSciNet)
MR3859371

Zentralblatt MATH identifier
06965414

Subjects
Primary: 65F30: Other matrix algorithms 65H10: Systems of equations

Keywords
multilinear PageRank tensor Newton-like method monotone convergence

Citation

Guo, Pei-Chang; Gao, Shi-Chen; Guo, Xiao-Xia. A Modified Newton Method for Multilinear PageRank. Taiwanese J. Math. 22 (2018), no. 5, 1161--1171. doi:10.11650/tjm/180303. https://projecteuclid.org/euclid.twjm/1521792084


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