# 网页排名PageRank算法初探+数学建模与求解

Exploration of Page Rank algorithm
Abstract：This article, with current Google’s search engine as the background, introduces positive matrix, some properties of column stochastic matrix, the relationship between eigenvalue and eigenvector and power iteration method which is used to calculate matrix eigenvalue through linear algebra as well as PageRank algorithm of Google search rating. By learning of PageRank algorithm, it is possible to download adjacent matrix of 500 websites which is related to home page of Harvard University on August 2003 and try to rank them.

Keywords: Linear Algebra; Positive matrix; Columns random matrix; Eigenvalue;  Eigenvectors; Power iteration method; PageRank algorithm; Adjacency matrix

1 引言 1
1.1 课题的目的和意义 1
1.2 国内外研究现状与发展趋势 2
1.3 文献综述 3
1.4 论文研究主要内容 4
1.4.1简化的PageRank算法 4
1.4.2改进的PageRank算法 5
1.4.3 PageRank算法—幂法 6
2 问题提出 7
3 数学基本概念的介绍 7
3.1基本数学概念的介绍 7
3.1.1有向图的定义 7
3.1.2邻接矩阵 8
3.1.3特征值和特征向量 8
3.1.4马尔可夫链 9
4 符号说明 10
5 数学建模与求解 10
5.1 PageRank算法原理及其应用 10
5.2改进的PageRank算法及其应用 13
5.3 PageRank算法-幂法的程序实现 14
5.4 实际问题解析 15
6 总结 22
7 致谢 23
8 参考文献 24,3449

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