Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
- 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
At the end of this learning unit, the student is able to :
With respect to the AA reference, this course contributes to the development, acquisition and evaluation of the following learning outcomes :
Transversal learning outcomes :
The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
- 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
- Classes organized following the EPL guidelines.
- Homeworks done individually
- A more detailed organization is specified each year in the course plan provided on Moodle.
Trefethen, L. N., & Bau III, D. Numerical linear algebra (Vol. 50). Siam.