ECTS
4 credits
Component
Faculty of Science
Description
This course will cover numerical methods applied to linear algebra and more particularly to matrices. The notions of conditioning, matrix decompositions and iterative methods, and eigenvalue computation will be introduced.
Objectives
Numerical solution of linear systems (problems, stability issues and algorithmic complexity) :
- elementary operations matrix, LU and Choleski factorization
- Matrix standards, packaging
- Iterative methods: Jacobi, Gauss-Seidel
- Convergence analysis: spectral radius
- Overdetermined systems : least squares methods and applications.
- Singular value decomposition and applications.
- Calculation of eigenvalues. Localization, link with the characteristic polynomial. Power and deflation methods.
Necessary pre-requisites
HAX102X - Algebra I Linear Systems
HAX202X - Algebra II Vector spaces and linear applications
HAX305X: Elementary numerical analysis
Recommended prerequisites: L1 math
Additional information
Hourly volumes:
CM : 15
TD : 10,5
TP : 15
Terrain: