Numerical analysis

linma1170  2023-2024  Louvain-la-Neuve

Numerical analysis
5.00 credits
30.0 h + 22.5 h
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 :

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 :
  • Analyze in depth the various key methods and algorithms for the numerical solution of important classes of problems from science and industry, related to applied mathematics  
  • Better understand the numerical behavior of the various numerical algorithms for the solution of linear as well as nonlinear problems
  • Implement these methods in a high level computer language and verify their numerical behavior on a practical problem
 Transversal learning outcomes :
  • Collaborate in a small team to solve a mathematical problem using numerical methods
  • 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)
Nous suivons relativement scrupuleusement l'excellent ouvrage :
Trefethen, L. N., & Bau III, D. Numerical linear algebra (Vol. 50). Siam.
Teaching materials
Faculty or entity

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Learning outcomes
Additionnal module in Mathematics

Minor in Applied Mathematics

Specialization track in Applied Mathematics

Mineure Polytechnique