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Hermite polynomials

  1. Apr 12, 2008 #1
    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 [Broken]
     
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Apr 12, 2008 #2

    Astronuc

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    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.
     
  4. Apr 12, 2008 #3
    i think given that argument for some groups of points with slopes the minimum curve that goes through both is a cubic.
     
  5. Apr 13, 2008 #4
    anyone?
     
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