A Modified Newton Method for Multilinear PageRank

被引：8

作者：

Guo, Pei-Chang ^{[1
]}

Gao, Shi-Chen ^{[1
]}

Guo, Xiao-Xia ^{[2
]}

机构：

[1] China Univ Geosci, Sch Sci, Beijing 100083, Peoples R China

[2] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2018年 / 22卷 / 05期

关键词：

multilinear PageRank; tensor; Newton-like method; monotone convergence; QUADRATIC VECTOR EQUATION; MARKOVIAN BINARY-TREES; SHAMANSKII METHOD; CONVERGENCE;

D O I：

10.11650/tjm/180303

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 < 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 > 1/2 we present an always-stochastic modified Newton iteration. Numerical results illustrate the effectiveness of this method.

引用

页码：1161 / 1171

页数：11

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