Numerical Analysis : Approximation, Interpolation, Integration [ LINMA2171 ]

• Approximation of functions by polynomials: Chebyshev (best approximation, polynomial series), L2 norm (best average approximation, orthogonal polynomial series, Fourier series).
• Interpolation of functions divided by polynomials: Lagrange and Newton formulas, divided differences, iterative methods of Neville, formulas of finished differences.
• Numerical integration: Gaussian methods, formulas of finished differences. 
• Error estimation and applications: Peano theorem, Euler-Maclaurin formula, extrapolation to the limit (Romberg scheme, etc.)

In-depth analysis of diverse methods and algorithms representative in the matter of numerical resolution by computers of significant classes of scientific or technical problems, in relation with the themes underlying the applied mathematics

1. Polynomial interpolation
2. Polynomial approximation in the maximum norm
3. Approximation in the 2-norm
4. Numerical integration
5. Piecewise polynomial approximation
6. Other topics related to the main themes

See http://icampus.uclouvain.be/