Teacher(s)
Language
French
Prerequisites
First cycle level in numerical calculus and programming (LEPL1104) and in linear algebra (LEPL1101).
Main themes
 Numerical methods for solving nonlinear equations
 Numerical methods for solving linear systems : iterative methods
 Numerical methods for solving eigenvalue and eigenvector problems
 Numerical solution of ordinary differential equations : initial value problems
Learning outcomes
At the end of this learning unit, the student is able to :  
1 
With respect to the AA reference, this course contributes to the development, acquisition and evaluation of the following learning outcomes : AA1.1, AA1.2, AA1.3 AA2.1, AA2.4 AA5.2, AA5.3, AA5.5 More precisely, after completing this course, the student will have the ability to :

Content
 Reminder of the basic notions of linear algebra (linear spaces, vector and matrix norms, ...)
 Floating point calculations.
 Stability, precision and conditioning of algorithms.
 QR and SVD factorizations.
 Linear systems of equations : direct methods. LU, Choleski, Pivoting, Renumbering (RCMK), direct resolution of sparse systems, Fillin.
 Iterative methods (Krylov subspaces) : iteration of Arnoldi, conjugate gradients, GMRES, Lanczos.
 Preconditioning of iterative methods, preconditioned conjugated gradients.
 Computing eigenvalues, QR algorithm
Teaching methods
 Classes organized following the EPL guidelines.
 Homeworks done individually
 A more detailed organization is specified each year in the course plan provided on Moodle.
Evaluation methods
Exam (50% of the grade) and homeworks (50% as well)
Online resources
Bibliography
 http://bookstore.siam.org/ot50/
Trefethen, L. N., & Bau III, D. Numerical linear algebra (Vol. 50). Siam.
Teaching materials
 http://bookstore.siam.org/ot50/
Faculty or entity