5. (Cubic Spline Overshoots)

Consider the test data x = {1, 2, 3, 3.1, 5.1, 6, 7, 8} and y = {1.8, 1.9, 1.7, 1.1, 1.1, 1.7, 1.4, 1.9}. Apply cubic spline interpolation to this data set using end/boundary condition types as discussed in this chapter (see equation (13.33)). Determine those subintervals in [1, 8] where negative values are produced. This is obviously an undesirable situation. In particular, what is the interpolated value when x = 4?

Carry out the same experiment with the data:

std::vector x = { 0,10,30.50,70,90,100 };

std::vector y = { 30,130,150,150,170,220,320};