求解PageRank向量的一种松弛多步分裂迭代方法
A Relaxed Multi-splitting Iteration Method for Computing PageRank Vector
田兆禄 1王玉栋 2刘仲云3
作者信息
- 1. 山西财经大学应用数学学院,太原 030006
- 2. 广西科技大学生物与化学工程学院,柳州 545006
- 3. 长沙理工大学数学与统计学院,长沙 410076
- 折叠
摘要
基于求解PageRank向量的内外迭代格式,引入一个松弛因子得到一种松弛内外迭代方法.结合已有的多步分裂迭代框架,引入两个不同的松弛因子,提出了求解PageRank向量的松弛多步分裂迭代方法并分析了算法的收敛性.更进一步地,利用松弛内外迭代格式构造了加速投影子空间方法的预处理矩阵,理论分析相关谱分布情况,并给出了松弛多步分裂迭代方法及预处理矩阵中参数的选取准则.几个数值例子验证了松弛多步分裂迭代方法和预处理矩阵的有效性,通过选取合适的松弛因子,与多步分裂迭代方法相比具有更高的运算效率.
Abstract
Based on the inner-outer iteration sequence for solving the PageRank vector,a re-laxed inner-outer iteration method is obtained by introducing a relaxed factor.Combining the multi-splitting iteration framework with two different relaxed factors,a relaxed multi-splitting iteration method for solving the PageRank vector is proposed,and its convergence property is analyzed.Furthermore,by using the relaxed inner-outer iteration format,a precon-ditioned matrix for accelerating the projection subspace methods is constructed,the spectral distribution is theoretically investigated,and choice criteria of the parameters in the relaxed multi-splitting iteration method and preconditioner are provided.Several numerical examples validate the effectiveness of the relaxed multi-splitting iteration method and preconditioner,the relaxed multi-splitting iteration method is more efficient compared to the multi-splitting iteration method with appropriate relaxed factors.
关键词
PageRank向量/多步分裂迭代方法/松弛因子/迭代矩阵/最优参数Key words
PageRank vector/multi-splitting iteration method/relaxed factor/iteration ma-trix/optimal parameter引用本文复制引用
基金项目
国家自然科学基金(52263002)
山西省自然科学基金(20210302123480)
山西省回国留学人员科研资助项目(2023-117)
出版年
2024
NETL
NSTL
万方数据