PageRank: new regularizations and simulation models

Abstract PageRank ( PR ) problem is one of the most challenging problems in information technologies and numerical analysis due to its huge dimension and wide range of applications. It also attracts great attention of experts in control theory; it is closely related to consensus in multiagent systems. The traditional approach to PR goes back to pioneering paper of Brin and Page. The original problem is replaced with finding eigenvector of modified matrix which can be effectively solved by power method. In this paper we demonstrate that the solution of the modified problem can be far enough from the original one and propose an iterative regularization method which allows to find the desired solution. We also present an l 1 -regularization which provides a solution with most low-ranking pages evaluated as zero-ranking. All methods are illustrated on two examples of PR problems which have many attractive features as simulation tests.