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 non-linear 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 : | |
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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 :
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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, Fill-in.
- 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
