Numerical Analysis : Approximation, Interpolation, Integration

linma2171  2023-2024  Louvain-la-Neuve

Numerical Analysis : Approximation, Interpolation, Integration
5.00 credits
30.0 h + 22.5 h
Q1
> Schedule
Teacher(s)
Absil Pierre-Antoine; Vary Simon (compensates Absil Pierre-Antoine);
Language
English
> French-friendly
Prerequisites
Basic skills in numerical methods, as covered, for example, within  LEPL1104 (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
  • Interpolation: polynomial, by spline functions, rational, trigonometric.
  • Orthogonal polynomials: Legendre polynomials, Chebyshev polynomials.
  • Approximation: uniform and in the least-square sense, by polynomials and by splines.
  • Numerical integration: Newton--Cotes formulas, Gauss 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
  • Work carried out during the term: homework assignments, exercises, or laboratory work. These activities are thus organized (and evaluated) only once per academic year.
  • Exam: written, or sometimes oral depending on the circumstances.
The final grade is min(2/5 D + 3/5 E, D+5, E+5), where D is the grade of the work carried out during the term and E is the grade of the exam.
Further information is provided in the "Course outline" document available on Moodle (see "Online resources" below).
Online resources
https://moodle.uclouvain.be/course/view.php?id=747
Bibliography
  • Textbook
  • Complementary documents posted on Moodle
Further information is provided in the "Course outline" document available on Moodle.
Faculty or entity
> MAP


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