Interpolation of Degree 1 by Intervals

This lecture covers the concept of interpolating a function of degree 1 over an interval. The instructor explains how to construct a continuous interpolating function that coincides with the original function at equidistant points within the interval. The theoretical result regarding the maximum error of the interpolation is also discussed, showing that the error is bounded by a constant times the square of the step size, independent of the function being interpolated. Numerical experiments confirm that the error decreases by a factor of 4 each time the step size is halved.