Numerical algorithms

The Numerical Algorithms module describes a range of methods and algorithms for modeling numerical problems.

Introduction to numerical computation: number representation and approximation problems, conditioning
Methods for solving linear systems: Gauss Cholesky A=LDL' Iterative methods: Jacobi Gauss-Seidel gradient relaxation
Least squares method : normal equation matrix factorizations
Eigenvalues and eigenvectors: reduction to tridiagonal form Givens bisection iterated power method
Solving nonlinear equations: iterative methods roots of polynomials case of dimension greater than 1
Numerical methods of interpolation and integration.
Differential equations: Cauchy problem Runge-Kutta method finite differences finite elements

Undergraduate mathematics (linear algebra, differential equations, etc.)

- Introduction to numerical computation: number representation and approximation problems, conditioning
- Methods for solving linear systems: Gauss Cholesky A=LDL' iterative methods: Jacobi Gauss-Seidel gradient relaxation
- Least squares method: normal equation matrix factorizations
- Eigenvalues and eigenvectors: reduction to tridiagonal form Givens bisection iterated power method
- Solving nonlinear equations: iterative methods polynomial roots case of dimension greater than 1
- Numerical methods of interpolation and integration.
- Differential equations: Cauchy problem Runge-Kutta method finite differences finite elements

Bibliographical references:

[1] P.Lascaux and 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: Numerical Analysis and Differential Equations - PUG

No course handout. A guide is available for some practical questions.