Hermite polynomials

  • Thread starter ice109
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  • #1
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Main Question or Discussion Point

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]
 
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Answers and Replies

  • #2
Astronuc
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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
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i think given that argument for some groups of points with slopes the minimum curve that goes through both is a cubic.
 
  • #4
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anyone?
 

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