Course Syllabus 2013/2014
 
PDF Extract Anglais
Français
index
Module : IS104
Title :
Numerical Analysis
Number of hours :
Combined lecture and tutorial classes : 48.00 h
Individual work : 18.00 h
ECTS credits :
4.00
Evaluation :
Teacher(s) :
RENAULT David - Responsible
Shared by UV(s) :
Level :
first year module
Abstract :
The course of Numerical Analysis presents a series of methods and algorithms dedicated to the modelisation of numerical problems.
Plan :
    • Introduction to numerical computations : problems of representation of numbers, approximation, conditioning
    • Methods of resolution of linear systems : Gauss ; Cholesky ; A=LDL'; iterative methods : Jacobi ; Gauss-Seidel ; relaxation ; gradient
    • Least squares method : normal equation ; factorisation of matrices
    • Eigenvalues and eigenvectors : reduction to tridiagonal form ; Givens method ; iterated power method
    • Resolution of non-linear equations : iterative methods, polynoms roots, stufy in dimension >= 2
    • Numerical methods for interpolation and integration
    • Differential equations : Cauchy problem ; Runge-Kutta method ; finite differences; finite elements
Prerequisite :
Undergraduate Mathematics (Linear Algebra, Differential equations ...)
Document(s) :
Bibliography :

[1] P.Lascaux et R.Théodor : Analyse numérique matricielle appliquée à l'art de l'ingénieur - Masson.

[2] W.H. Press et al. : Numerical Recipes in C, the art of scientific computing - Cambridge University Press.

[3] J.P. Demailly : Analyse Numérique et Equations différentielles - PUG

No lecture notes. A guide is available to explain the rules for the projects.

Keyword(s) :
complexity, Gauss method, matrix factorization, relaxation, gradient, numerical approximation, condition number, Givens, Householder, Horner, least squares, Runge-Kutta, intepolation
Online course :