ECTS
4 credits
Component
Faculty of Science
Description
This course deals with numerical methods applied to linear algebra, and more specifically to matrices. The notions of conditioning, matrix decompositions and iterative methods, and the calculation of eigenvalues will be introduced.
Objectives
Numerical solution of linear systems (problems, stability issues and algorithmic complexity) :
- elementary operation matrix, LU and Choleski factorization
- Matrix standards, conditioning
- 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 characteristic polynomial. Power and deflation methods.
Necessary prerequisites
HAX102X - Algebra I Linear systems
HAX202X - Algebra II Vector spaces and linear applications
HAX305X: Elementary numerical analysis
Recommended prerequisites: L1 maths
Further information
Hourly volumes :
CM: 15
TD: 10.5
TP: 15
Terrain :