The problems in finding the PageRank vector, used by Google to rank web pages, have attracted attention of mathematics
community during the last ten years. Different aspects of study include reasoning behind the PageRank approach, formation of the original stochastic matrix, use of personalization vector, and application of different numerical algorithms.

In this study we present an analysis of convergence properties for a general algorithm of computation of the PageRank vector.
It is shown that the convergence to the PageRank vector is generally nonuniform. Expressions for the limiting forms of the principal matrix of the PageRank approximation and the PageRank vector are derived in terms of the original stochastic matrix and the personalization vector.