A Note on the Eigenvalues of the Google Matrix
Lars Eldén
Google矩阵是一个正的列随机矩阵,用于计算互联网上所有网页的页数:与特征值1相对应的特征向量是页面向量。 由于其巨大的维度,数十亿的顺序,(目前)唯一可行的方法来计算特征向量是功率方法。 对于迭代的收敛,了解矩阵的特征值分布至关重要。 最近,朗维尔和迈耶证明了一个关于特征值的定理。 在这个说明中给出了另一个证据。
The Google matrix is a positive, column-stochastic matrix that is used to compute the pagerank of all the web pages on the Internet: the eigenvector corresponding to the eigenvalue 1 is the pagerank vector. Due to its huge dimension, of the order of billions, the (presently) only viable method to compute the eigenvector is the power method. For the convergence of the iteration, it is essential to know the eigenvalue distribution of the matrix. A theorem concerning the eigenvalues was recently pr...