Updating pagerank with iterative aggregation
To our knowledge, there are several kinds of extrapolation methods, such as quadratic extrapolation , two polynomial-type methods including the minimal polynomial extrapolation method (MPE) of Cabay and Jackson  and the reduced rank extrapolation (RRE) of Eddy , and the three epsilon vector extrapolation methods of Wynn .
In recent years, many papers have discussed the application of vector extrapolation method to compute the stationary probability vector of Markov chains and web ranking problems, see [6, 8, 9, 22, 23, 27] for details.
Now there are many acceleration algorithms for Page Rank computation, and among all the algorithms the vector extrapolation method is a very popular and efficient one.
The remainder of this paper is organized as follows.Due to the large size of the web graph (over eight billion nodes ), computing Page Rank is faced with the big challenge of computational resources, both in terms of the space of CPU and RAM required and in terms of the speed of updating in time; that is, as a new crawl is completed, it can be soon available for searching.Among all the numerical methods to compute Page Rank, the Power method is one of the standard ways for its stable and reliable performances , whereas the low rate of convergence is its fatal flaw.We show how to periodically combine the extrapolation method together with the multilevel aggregation method on the finest level for speeding up the Page Rank computation.
Detailed numerical results are given to illustrate the behavior of this method, and comparisons with the typical methods are also made.
However, aggregation/disaggregation cannot always dissolve the algorithmic scalability due to poor approximation of in problem (2) by unsmoothed intergrid operators, so a careful choice of aggregation strategy is crucial for the efficiency of the multilevel aggregation hierarchies.