The goal of this project is to assess problems that can arise when using elementary operations, or even more advanced algorithms, on floating point numbers.
http://mfaverge.vvv.enseirb-matmeca.fr/wordpress/?page_id=286
- Michel Théo
- Lamhamdi Aymane
- Dieu Killian
- Guedon Mathilde
- Kasour Mahmoud
The resolution of linear systems is a common problem present in many fields of research such as heat diffusion. This resolution is done on systems of consequent size which can contain thousands of equations. Several methods of resolution exist such as the method of the Gaussian pivot. Although we know how to solve many of these systems of equations, two other problems arise, that of the resolution in a reasonable time and that of the memory space occupied by the problem. We will devote ourselves in a first part to the Cholesky factorization method adapted to certain linear systems. Then we will study a second method called the conjugate gradient method. Finally, we will apply part of our methods of solving systems to solve particular cases of the problem of heat diffusion in two dimensions.
http://mfaverge.vvv.enseirb-matmeca.fr/wordpress/?page_id=293
- Meurgues Juliette
- Belamrabet Marouane
- Guerin Léo
- Lamhamdi Aymane
- Pitault Timothé
This project consists in programming an algorithm allowing to perform image compression using matrix techniques based on SVD factorization. The first part sets up the utility functions to manipulate the Householder matrices. The second and third part consist in transforming a matrix into a bidiagonal matrix then into a diagonal matrix. The last part applies these transformations to the SVD transformation image compression algorithm.
http://mfaverge.vvv.enseirb-matmeca.fr/wordpress/?page_id=298
- Pitault Timothé
- Meurgues Juliette
- Guedon Mathilde
- Lamhamdi Aymane
- Liard Arthur