# Cardinal B-Splines with derivative information

Have Schoenberg's cardinal B-splines been extended to accept derivative information at each knot, similar to how Lagrange interpolation can be improved by Hermite interpolation?

• What do you mean by "accept derivative information"? Do you want to interpolate data with a B-spline and match first derivatives? – vibe Mar 1 '19 at 0:01
• @vibe: Yes, the goal is to build a better interpolator if I have $y_i$ and $y_i'$ at each knot. – user14717 Mar 1 '19 at 0:13
• You can construct the Hermite interpolant, which uses $(x,y,dy/dx)$ data input by using an appropriate knot vector and imposing the continuity conditions of the function value and its derivative at each knot interface. See section 5.1.2 of folk.uio.no/in329/nchap5.pdf – vibe Mar 2 '19 at 1:08