求解PageRank问题的重启GMRES修正的多分裂迭代法  

A Modified Multi-Splitting Iterative Method With the Restarted GMRES to Solve the PageRank Problem

作　　者：肖文可 陈星玎[1] XIAO Wenke;CHEN Xingding(School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,P.R.China)

机构地区：[1]北京工商大学数学与统计学院,北京100048

出　　处：《应用数学和力学》2022年第3期330-340,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12071469)。

摘　　要：PageRank算法已经成为网络搜索引擎的核心技术.针对PageRank问题导出的线性方程组,首先将Krylov子空间方法中的重启GMRES(generalized minimal residual)方法与多分裂迭代(multi-splitting iteration,MSI)方法相结合,提出了一种重启GMRES修正的多分裂迭代法;然后,给出了该算法的详细计算流程和收敛性分析;最后,通过数值实验验证了该算法的有效性.The PageRank algorithm has become the core technology for web search engines.For the linear equations derived from the PageRank problem,firstly,the restarted GMRES(generalized minimal residual)method of the Krylov subspace methods was combined with the multi-splitting iterative method,and a modified multi-splitting iterative method with the restarted GMRES was proposed.Then,the detailed calculating process and the convergence analysis of this new algorithm were given.Finally,the effectiveness of the algorithm was demonstrated through some numerical experiments.

关 键 词：PAGERANK 重启GMRES方法 多分裂迭代法 收敛性 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] O242.2[自动化与计算机技术—计算机科学与技术]