Conclusions
The Ranking of Nodes in Networks

Here we've presented the problem of ranking Web pages in order of importance. This ranking is based on the PageRank algorithm developed by the creators of Google. We reviewed the fundamental ideas behind this algorithm, discussed the power method for its implementation and highlighted its difficulties. We then showed how to accelerate convergence and extrapolate the resulting vectors. It's important to understand, however, that this algorithm is only one of those used in search engines. We don't even know if it's still in use today, as this field is covered by industrial secrecy. The question has, however, been widely studied by the numerical linear algebra community. Indeed, the same type of problem is encountered in other areas of applied mathematics. In any case, it's a great example to illustrate numerical analysis courses on calculating the eigenelements of a matrix!

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