Investigating Googles Page Rank Algorithm Iterations for Convergence

Investigating Google’s Page. Rank Algorithm Iterations for Convergence The Power method requires far more iterations to converge than the Arnoldi method. Researchers: Erik Andersson eran 3133@student. uu. se Page. Rank Explained A page is important if other important pages link to it. This is an eigenvector problem: Per-Anders Ekström peek 5081@student. uu. se The matrix Q describes the link structure. To assure a reasonable answer Q must be modified. Advisors: Lars Eldén laeld@math. liu. se Maya G. Neytcheva maya@it. uu. se Execution Time The time for convergence is better for the restarted Arnoldi method than other tested methods. As alpha increases this difference becomes more evident. Here d shows which pages lack outlinks and alpha determines the general probability of “teleporting” to a random Web page. Eigenvector methods used Power method + low memory demands – slow for large alpha-values Arnoldi method + few iterations for convergence – high memory demands – increasing work for each iteration Restarted Arnoldi + fast for all alpha-values ± much less memory needed than for normal Arnold, but higher than the Power method Web-Crawler Written in Perl and used to retrieve the link structure of a specified domain. Example The following small 6 page link structure would give us the following Q. This is the link structure of it. uu. se. Contact: Lina von Sydow Lina. von. Sydow@it. uu. se Project in course ”Scientific Computing 10 p. ” at the Division of Scientific Computing, Department of Information Technology, Uppsala University