Fiches de cours 2017-2018

PDF
 

Advanced numerical analysis

MATH-351

Enseignant(s) :

Picasso Marco

Langue:

English

Summary

The student will learn state-of-the-art algorithms for solving ordinary differential equations, nonlinear systems, and optimization problems. Moreover, the analysis of these algorithms and their efficient implementation will be discussed in some detail.

Content

Numerical Solution of Ordinary Differential Equations

Runge-Kutta methods. Order 4 conditions. Step size control. Convergence.

Nonlinear systems of equations

Solution of large-scale linear and nonlinear systems.

Numerical Optimization

Newton, BFGS and conjugate gradient methods. Constrained optimization problems. Quadratic programming.

Keywords

Ordinary differential equations, adaptive methods, nonlinear solvers, optimization, large-scale problems.

Learning Prerequisites

Recommended courses

Some background in numerical analysis and proficiency in programming - Matlab recommended

Important concepts to start the course

Numerical methods for approximation, differentiation and integration of functions. Basic knowledge of ordinary differential equations and their solutions. Basic knowledge of numerical techniques for solving systems of linear equations.

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Lecture style with computational experiments in class to illustrate analysis.

Expected student activities

Students are expected to attend lectures and participate actively in class and exercises. Exercises will include both theoretical work and implementation and test of a variety of methods.

Assessment methods

Written examination.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

Bibliography

Lecture notes will be provided by the instructor. Complimentary reading:

Hairer, E.; Norsett, S. P.; Wanner, G. Solving ordinary differential equations. I. Springer, 1987.

Nocedal, J.; Wright, S. J. Numerical optimization. Second edition. Springer, 2006

Ressources en bibliothèque

Dans les plans d'études

  • Mathématiques, 2017-2018, Bachelor semestre 5
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Advanced numerical analysis
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Science et ingénierie computationnelles, 2017-2018, Master semestre 1
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Advanced numerical analysis
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines
  • Science et ingénierie computationnelles, 2017-2018, Master semestre 3
    • Semestre
      Automne
    • Forme de l'examen
      Ecrit
    • Crédits
      5
    • Matière examinée
      Advanced numerical analysis
    • Cours
      2 Heure(s) hebdo x 14 semaines
    • Exercices
      2 Heure(s) hebdo x 14 semaines

Semaine de référence

LuMaMeJeVe
8-9MAA331
9-10
10-11 MAA330
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Cours
Exercice, TP
Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand