Numerical Analysis : Approximation, Interpolation, Integration [ LINMA2171 ]

> https://icampus.uclouvain.be/claroline/course/index.php?cid=LINMA2171

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.

• Interpolation
• Function approximation
• Numerical integration

• 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.

• 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

• Lectures
• Homeworks, exercises, or laboratory work under the supervision of the teaching assistants

• 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.

• Reference book
• Complementary documents posted on iCampus

Precisions are given in the course outline (plan de cours) available on iCampus.