Numerical analysis

linma1170  2018-2019  Louvain-la-Neuve

Numerical analysis
5 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Henrotte François (compensates Remacle Jean-François); Remacle Jean-François;
Language
French
Prerequisites
First cycle level in numerical calculus and programming (LFSAB1104) and in linear algebra (LFSAB1101).

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
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
Aims

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
 

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”.
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

https://moodleucl.uclouvain.be/course/view.php?id=10034
 
Bibliography
  • http://bookstore.siam.org/ot50/
Nous suivons relativement scrupuleusement l'excellent ouvrage :
Trefethen, L. N., & Bau III, D. Numerical linear algebra (Vol. 50). Siam.
Teaching materials
  • http://bookstore.siam.org/ot50/
Faculty or entity
MAP


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

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Mathematics
MATH2M
5
Master [120] in Statistic: General
STAT2M
5
Bachelor in Engineering
FSA1BA
5
LEPL1104
Minor in Engineering Sciences: Applied Mathematics
LMAP100I
5
Additionnal module in Mathematics
LMATH100P
5