• ECTS

    3 credits

  • Component

    Faculty of Science

Description

In this course, the particularities of floating-point calculus will be discussed, followed by details of the usual elementary numerical methods for solving nonlinear equations, interpolating a function and approximating an integral. The student will learn how to implement an algorithm to solve a numerical analysis problem.

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Objectives

Particularities of the floating-point calculation: relative precision and IEEE format.

  Solving non-linear equations f(x)=0

  • Intermediate value theorem, dichotomy
  • Method of the contracting fixed point. Speed of convergence.
  • Newton and secant. Speed of convergence.

 Polynomial interpolation.

  • existence and uniqueness of the interpolation polynomial
  • interpolation error, generalized finite increase theorem
  • Runge's 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
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Necessary pre-requisites

The analysis courses of L1 (HAX103X and HAX201X) and some notions of linear algebra (HAX102X) are sufficient to integrate this UE.

 

Recommended prerequisites: L1 math

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Additional information

Hourly volumes* :

            CM : 12

            TD : 9

            TP : 9

            Terrain:

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