Interpolation de degré 2 par intervalles

This lecture covers the construction of a piecewise continuous function that coincides with a given function at equidistant points and midpoints, and is a degree 2 polynomial within each interval. The instructor demonstrates the process step by step, showing how the resulting function is continuous but not C1 at the breakpoints. The lecture concludes with a discussion on the convergence of the error towards zero as the distance between points approaches zero, supported by Theorem 1.2. Theoretical bounds on the maximum error are derived, highlighting the relationship between the error, the function's continuity, and the interval length. Numerical experiments illustrate how the error decreases by a factor of 8 when the interval size is halved.