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During year 2004/2005, i followed the DEA **analyse numerique** from the university of [Paris VI](http://www.upmc.fr). This is now called [parcours Analyse Numérique & Équations aux Dérivées Partielles](http://www.ann.jussieu.fr/ANEDP).
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During year 2004/2005, i followed the DEA **analyse numerique** from **Université Pierre & Marie Curie, Paris VI**, now part of [Sorbonne Université](https://www.sorbonne-universite.fr) [Paris VI](http://www.upmc.fr). This is now called [parcours Analyse Numérique & Équations aux Dérivées Partielles](https://www.ljll.math.upmc.fr/MathModel/presentation/anedp.html).
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The last chapters are in French.
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## Research Internship
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The last chapters are in French.
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## Research Internship
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I worked on a new way of doing multiscale image analysis. The idea was to use the knowledege about disocclusion or [inpainting](http://en.wikipedia.org/wiki/Inpainting) in order to predict the image at a lower lower. One application could be find new compression algorithm. My advisors were [Albert Cohen](http://www.ann.jussieu.fr/\~cohen/) and [Simon Masnou](http://www.ann.jussieu.fr/\~masnou/).
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I worked on a new way of doing multiscale image analysis. The idea was to use the knowledege about disocclusion or [inpainting](http://en.wikipedia.org/wiki/Inpainting) in order to predict the image at a lower lower. One application could be find new compression algorithm. My advisors were [Albert Cohen](https://www.ljll.math.upmc.fr/cohen/) and Simon Masnou.
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[Read my report (English)](http://www.freehackers.org/media/orzel/dea/stage/rapport.pdf)
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`Run program 5.1 to 5.5. Adapt it to a barrier option with realistic data. If times allow make the change S -> S/(S+1) which maps R+ into (0,1) and compute a European put in this formulation and compare.`
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- [Rapport du projet](http://www.freehackers.org/media/orzel/dea/finance/rapport_finance.pdf)
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- [Code source du projet (bz2)](http://www.freehackers.org/media/orzel/dea/finance/sources-finance.tar.bz2)
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- [Code source du projet (tar.gz)](http://www.freehackers.org/media/orzel/dea/finance/sources-finance.tar.gz)
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J'ajoute un test en fin de programme qui calcule le max des différences entre les températures obtenues, et celles que j'aurais dû obtenir. Voici le code
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```
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```plaintext
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// test de validité
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R max = 0.;
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R tetamax =0.;
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Pour modifier la matrice globale, je n'ai pas trouvé de fonction correspondante dans l'API de fem, j'ai donc rajouté la fonction Add2x2Matrice aux fichiers MatriceCreuse_tpl.hpp et MatriceCreuse.hpp, dont voici le code (clairement inspiré de la fonction operator+=)
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```
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```plaintext
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template<class R> MatriceCreuse<R> & MatriceProfile<R>::add2x2Matrice (int i0, int i1,R a00, R a01, R a11)
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{
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int i,j;
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