Hermite polynomials

1. Apr 12, 2008

ice109

are hermite interpolationg polynomials necessarily cubic even when used to interpolate between two points?

this page would have me believe so in calling it a "clamped cubic" :

http://math.fullerton.edu/mathews/n2003/HermitePolyMod.html

2. Apr 12, 2008

Staff: Mentor

It's more the case that there exists a cubic polynomial of the form:

a x3 + b x2 + c x + d, which satisfies the constraints at two points, (x0, y0) and (x1, y1), where

p(x0) = f(x0) = y0

p(x1) = f(x1) = y1

and

p'(x0) = f'(x0) = y'0

p'(x1) = f'(x1) = y'1

4 equations, and 4 unknowns (a, b, c, d)

This is the basis of the cubic spline.

3. Apr 12, 2008

ice109

i think given that argument for some groups of points with slopes the minimum curve that goes through both is a cubic.

4. Apr 13, 2008

anyone?