# How Google is working and how to improve it

ARGOMENTI: Convegni

Martedi' 23 gennaio 2007, alle ore 16:00, in aula 1C/50, il Professor Claude BREZINSKI dell'Universita' di Lille terra' (in inglese) un seminario di base sul calcolo del Pagerank di Google (e sulle tecniche di accelerazione e di estrapolazione dello stesso) utilizzando metodologie di Analisi Numerica.

Il seminario e' volto a tutti coloro che sono interessati a conoscere maggiormente tale tematica di cui si e' anche parlato lo scorso 16 gennaio 2007 durante la quarta conferenza dei Colloquia Patavina.

- Abstract
The mathematical problem behind web search is the computation of the nonnegative left eigenvector (the PageRank) of a matrix of dimension 8.06 billions.
The mathematical problem, and the properties of this vector will be discussed.
This vector is computed by the power method as the dominant eigenvector of a matrix depending of a parameter $c$ tending to 1. The method will be analyzed in this context.
Then, we will show how the convergence of the power method could be accelerated.
Finally, computing the PageRank for different values of $c$, several extrapolation procedures will be proposed, and
numerical results will be given.

- Short Biography
Claude Brezinski is Professor Emeritus at the University of Sciences and technologies of Lille (France). For around 30 years, he was the head of the Laboratory of Numerical Analysis and Optimization.
He is the author of 17 books, and 185 research papers. They concern approximation, linear algebra, extrapolation, linear algebra, orthogonal polynomials, and history.
He is the founder and editor-in-chief of the journal Numerical Algorithms, and belongs to the editorial board of several journals.

Rif. M. Redivo Zaglia