# Numerical Analysis : Approximation, Interpolation, Integration

linma2171  2018-2019  Louvain-la-Neuve

Numerical Analysis : Approximation, Interpolation, Integration
5 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.

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
• Interpolation
• Function approximation
• Numerical integration
Aims
 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.

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
• 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 iCampus > LINMA2171 > Documents et liens
Online resources
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
Aims
Master [120] in Data Science Engineering

Master [120] in Statistic: General

Master [120] in Mathematical Engineering

Bachelor in Mathematics

Master [120] in data Science: Information technology