Note from June 29, 2020
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.
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.
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.
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
Aims
At the end of this learning unit, the student is able to : | |
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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
Online resources
Bibliography
- Ouvrage de référence
- Documents complémentaires disponibles sur Moodle.
Faculty or entity
MAP
