1
$\begingroup$

I am trying to interpolate monotone data with known data values and also known first derivative values at knots. If I used these values with cubic Hermite spline interpolation, Can I guarantee the monotonicity of the interpolation segments?

$\endgroup$
  • $\begingroup$ Cannot answer, depends on the given slopes. $\endgroup$ – Yves Daoust Jan 17 at 10:18
  • $\begingroup$ As noted, the condition of being $C^2$ forces you to sacrifice monotonicity in your cubic spline. That being said, there are $C^2$ rational interpolants that also possess monotonicity. You might try researching about them if this is of interest. $\endgroup$ – J. M. isn't a mathematician Mar 30 at 12:50
1
$\begingroup$

No, straightforward Hermite cubic interpolation does not guarantee monotonicity. However, there are other piecewise polynomial interpolation methods that do preserve monotonicity. Look up terms like "monotone spline" or "monotone interpolation". Here is one reference, which describes the Fritsch-Carlson method.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.