Numerical Analysis : Approximation, Interpolation, Integration

linma2171  2021-2022  Louvain-la-Neuve

Numerical Analysis : Approximation, Interpolation, Integration
5.00 credits
30.0 h + 22.5 h
Q1
Teacher(s)
Absil Pierre-Antoine;
Language
English
Prerequisites
Basic skills in numerical methods, as covered, for example, within  LFSAB1104 (Numerical methods).
Remark : LINMA2171 is the second part of a teaching programme in numerical analysis, of which LINMA1170 is the first part ; however, LINMA1170 is not a prerequisite for LINMA2171.
Main themes
  • Interpolation
  • Function approximation
  • Numerical integration
Learning outcomes

At the end of this learning unit, the student is able to :

1
  • AA1.1, AA1.2, AA1.3
At the end of the course, the student will be able to:
  • Implement, in concrete problems, the basic knowledge required from an advanced user and a developer of numerical computing software;
  • Analyze in depth various methods and algorithms for numerically solving scientific or technical problems, related in particular to interpolation, approximation, and integration of functions.
Transversal learning outcomes :
  • Use a reference book in English;
  • Use programming languages for scientific computing.
 
Content
  • Polynomial interpolation: Lagrange's interpolation formula, Neville's algorithm, Newton's interpolation formula, divided differences, Hermite interpolation.
  • Interpolation by spline functions : cubic spline interpolation, B-splines.
  • Rational interpolation.
  • Trigonometric interpolation.
  • Orthogonal polynomials : Legendre polynomials, Chebyshev polynomials.
  • Polynomial minimax approximation : existence, de la Vallée-Poussin's theorem, equioscillation theorem, uniqueness, Chebyshev interpolation.
  • Polynomial approximation in the least-squares sense.
  • Numerical integration : Newton-Cotes formula, Gauss method.
  • Integration of differential equations : introduction to the finite element method.
  • Other topics related to the course themes.
Teaching methods
  • Lectures
  • Homeworks, exercises, or laboratory work under the supervision of the teaching assistants
Evaluation methods
  • Homeworks, exercises, or laboratory work during the course semester
  • Exam
Precisions are given in the course outline (plan de cours) available on Moodle.
Online resources
https://moodle.uclouvain.be/course/view.php?id=747
Bibliography
  • Ouvrage de référence
  • Documents complémentaires disponibles sur Moodle.
Des précisions sont fournies dans le plan de cours disponible sur Moodle.
Faculty or entity
MAP


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

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Data Science Engineering
DATE2M
5
Master [120] in Mathematics
MATH2M
5
Master [120] in Data Science: Information Technology
DATI2M
5
Master [120] in Mathematical Engineering
MAP2M
5