I have a problem with divided differences.
Let f be a function such as . Find a polynom of degree minor or equal to 3 that satisfy :
I think I have to make a table of divided difference. My problem is how do I deal the table when I have a condition on a derivate, such as p'(1)=f'(1). And how can I deal with double derivate conditions?
Because I think that it would not interpolate the data I gave. It would be preciser on one point while what I need is a polynom passing by a set of points coinciding with a known function and also satisfying that its derivative pass by some points as the derivative of the known function do.