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

作　　者：田兆禄 王玉栋 刘仲云 TIAN Zhaolu;WANG Yudong;LIU Zhongyun(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006;College of Biological and Chemical Engineering,Guangxi University of Science and Technology,Liuzhou 545006;School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410076)

机构地区：[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

出　　处：《工程数学学报》2024年第4期642-658,共17页Chinese Journal of Engineering Mathematics

基　　金：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).

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。Based on the inner-outer iteration sequence for solving the PageRank vector,a relaxed inner-outer iteration method is obtained by introducing a relaxed factor.Combining the multi-splitting iteration framework with two different relaxed factors,a relaxed multisplitting 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 preconditioned 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 

分 类 号：O241.6[理学—计算数学]