C++ for Scientists - Technische Universität Dresden

274 CHAPTER 14. NUMERICAL EXERCISES
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Figure 14.2: An example of a web with only four pages. An arrow from page A to page B
indicates a link from page A to page B.
or
with
14.3.4 Exercise
du
dt
= f(u)
f(u) = −A(u)u .
Use the Runge-Kutta 4 method for evaluating the Van der Pol equation for µ = 0, µ = 0.1 and
µ = 1 in the time interval [0, 10] with time steps h = 0.001. Also try smaller and larger time
steps.
Plot the results using gnuplot.
14.4 Google’s Page rank
We all use Google for web searching. In this exercise, we try and understand a particular tool
used by Google to rank pages, called PageRank.
The basic idea behind the Google Page Ranking Algorithm, is that the importance of a webpage
is determined by the number of references made to it. We would like to compute a score xk
reflecting the importance of page k. A simple minded approach would be just to count the
number of links to each page. This approach does not reflect the fact that some pages might
be more significant than others therefore rendering their votes more important. It also leaves
open the possibility of artificially inflating the rank of a particular page by generating other
trivial or advertising pages whose only function is to promote the importance of a particular
page. Significant refinements are:
• Weight each in-link by the importance of the page which links to it.
• Give each page a total vote of 1. If page j contains nj links, one of which links to page k,
then page k’s score is boosted by xj
nj .
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