Elementary numerical analysis

This course will cover the particularities of floating-point arithmetic, then detail common elementary numerical methods for solving nonlinear equations, interpolating a function, and approximating an integral. Students will learn how to implement an algorithm for solving a numerical analysis problem.

Special features of floating-point arithmetic: relative precision and IEEE format.

  Solving nonlinear equations f(x)=0

• Intermediate values theorem, dichotomy
• Contracting fixed point method. Convergence speed.
• Newton and secant. Convergence speed.

 Polynomial interpolation.

• existence and uniqueness of the interpolation polynomial
• interpolation error, generalized finite increment theorem
• Runge phenomenon
• Lagrange polynomial, Newton polynomial, and divided differences
• Application to digital derivation
• Hermite interpolation

  Digital integration.

• Newton's methods (midpoint, trapezoidal, Simpson's, etc.)
• order of a quadrature method. Estimation of
• Monte Carlo method
• Gauss method: optimal order, example of Gauss-Legendre

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

Recommended prerequisites: L1 maths

Hourly volumes:

            CM: 12

            TD: 9

            TP: 9

            Land: