Regularization-based solution of the PageRank problem for large matrices

For a column‐stochastic matrix, consideration was given to determination of the eigenvector which corresponds to the unit eigenvalue. Such problems are encountered in many applications,–in particular, at ranking the web pages (PageRank). Since the PageRank problem is of special interest for larger matrices, the emphasis was made on the power method for direct iterative calculation of the eigenvector. Several variants of regularization of the power methods were compared, and their relations were considered. The distinctions of their realizations were given.