Pagerank Methods Accelerated With The Thick-restarted Arnoldi

With the fast development of the Internet, the expansion of the network information, web search eigines have become the most commonly used tools for retrieving information. How to find useful information among the massive and messy information quickly and ac-curately have become a common concern that scholars are pursuing. Web page ranking is one of the key technology of search engine, its quality will directly affect the accuracy on retrieving information for the Internet users.In the current search engine ranking algorithm-s, one of the most successful algorithms is the PageRank algorithm developed by Larry and Sergey Brin of Stanford university in 1996.It is used to evaluate the importance of a web page ranking level.The PageRank problem can be converted to solve the pricipal eigenvector of the Google matrix.The original PageRank algorithm uses the Power method to compute the principal eigenvector of the Google matrix. On the other hand, the PageRank problem can also be sloved through the large sparse linear systems. Meanwhile, a large number of the Krylov subspace methods can also be used for accelerating the computation of the PageRank prob-lem.Based on the inner-outer iteration method, the MSI method, we analyze the thought of precondition and present the thick restarted Arnoldi algorithm accelerated with the inner-outer iteration method and the thick restarted Arnoldi algorithm accelerated with the MSI method to compute the PageRank problem. In Section 4, we combine the merits of the thick-restarted Arnoldi and the inner-outer iteration method and first run the thick restarted Arnoldi algorithm to get a rough approximation, then iterate the inner-outer iteration method to get another approximation. If the result is still unsatisfactory, return to the thick restarted Arnoldi method. Proceeding the above procedure analogously until the described accuracy is achieved. In Section 5, we present a MSI method accelerated with the thick restarted Arnoldi method. Numerical examples are shown in Section 4 and 5 to verify our theoretical results and illustrate the efficiency of the new method.