ECTS
3 credits
Component
Faculty of Science
Description
In this course, we'll look at the particularities of floating-point calculus and then go into detail on the most common elementary numerical methods for solving non-linear equations, interpolating a function and approximating an integral. Students will learn how to implement an algorithm to solve a numerical analysis problem.
Objectives
Special features of floating-point calculation: relative precision and IEEE format.
Solving non-linear equations f(x)=0
- Intermediate value theorem, dichotomy
- Contracting fixed point method. Speed of convergence.
- Newton and secant. Speed of convergence.
Polynomial interpolation.
- existence and uniqueness of the interpolation polynomial
- interpolation error, generalized finite theorem
- Runge phenomenon
- Lagrange polynomial, Newton polynomial and divided differences
- Application to numerical derivation
- Hermite interpolation
Numerical integration.
- Newton's methods Dimensions (midpoint, trapezoids, Simpson, etc.)
- order of a quadrature method. Estimation of
- Monte Carlo method
- Gauss method: optimal order, Gauss-Legendre example
Necessary prerequisites
The analysis courses of L1 (HAX103X and HAX201X) and a few notions of linear algebra (HAX102X) are sufficient to integrate this UE.
Recommended prerequisites: L1 maths
Further information
Hourly volumes* :
CM : 12
TD : 9
TP: 9
Terrain :