Numerical analysis : tools and software of calculus [ LMAT1151 ]

Sources of errors in numerical analysis, propagation of errors.
Direct and iterative methods for the resolution of linear systems.
Numerical resolution of non-linear systems.
Numerical integration.
Part of the exercices will be devoted to the study of a computer program 
in numerical analysis. This activity will lead to a project for which a 
numerical problem has to be solved using the computer program. This 
course gives also the opportunity to give numerical solutions to 
problems met in other courses.

The goal of the course is the presentation and discussion of basic 
methods for the numerical resolutions of problems, in particular for 
solving equations. Besides the construction of numerical methods 
starting from basic principles, the course will contain an introduction 
to the analysis of errors and to the evaluations of the efficiency of 
methods. Summarizing, the aim is to understand why and how the methods 
work, which are the limitations and which precision one can expect. This 
should enable the students to use programs and software used in 
numerical computations.

The evaluation will be made on the basis of a written exam and a project 
realized during the year.

The following subjects will be considered: calculus of errors, direct 
and iterative methods of resolutions of linear systems, numerical 
resolution of non-linear systems, numerical integration.

A. Quarteroni, R. Sacco, L. Saleri, Méthodes numériques pour le 
calcul scientifique