Lectures in course MATH-251(d): Numerical analysis

Covers iterative methods for solving linear systems of equations and discusses the convergence properties of methods like Richardson's method.

Provides an overview of the Numerical Analysis course at EPFL, focusing on course organization, materials, and learning outcomes.

Explores floating point numbers, their representation, precision, and associated errors.

Explores the bisection method for solving non-linear equations with a focus on error control and MATLAB implementation.

Explores fixed point methods for non-linear equations and dynamic models in MATLAB.

Discusses fixed-point methods, convergence analysis, error control, and high-order methods.

Covers fixed-point methods and Newton-Raphson, emphasizing their convergence and error control.

Explores systems of non-linear equations and polynomial interpolation, including the Newton method and Vandermonde matrix construction.

Explores polynomial interpolation, Lagrange polynomials, and the challenges of interpolation methods.

Covers polynomial interpolation, error analysis, stability, and piecewise linear interpolation using equally distributed nodes.

Covers piecewise linear and spline interpolation methods, stability, convergence, and data interpolation using splines.

Explores cubic splines and least-squares approximation, focusing on interpolation methods and error analysis.

Covers polynomial interpolation and least-squares approximations to minimize errors.

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Explores numerical differentiation methods and round-off errors in computer computations.

Explores numerical integration through quadrature formulas and composite Simpson's formula.

Explores numerical integration methods and error analysis in approximating definite integrals.

Covers direct methods for solving linear equations and computation complexity of substitution.

Explores direct methods for solving linear equations, LU factorization, Gass elimination, and computational complexity.