why does not "pchip" requires derivative values as input

8 次查看（过去 30 天）
Xinwei Li
Xinwei Li 2023-10-20
编辑： Bruno Luong 2023-10-20
In my understanding, Piecewise Cubic Hermite polynomials requires both values and derivative values at each point.
Matlab "pchip", https://www.mathworks.com/help/matlab/ref/pchip.html, is exactly Piecewise Cubic Hermite polynomials, but does not require derivatives.
So why no derivatives values are needed as inputs for "pchip"

请先登录，再回答此问题。

回答（1 个）

Bruno Luong
Bruno Luong 2023-10-20
编辑：Bruno Luong 2023-10-20
Since the derivatives are computed internally as with general polynomial picewise functions.
It satisfies :
  • interpolation on data point
  • The derivative inside the interval does not change sign (hermit specific), but this constraints are enforced internally
If user imposes the derivarive at the break points then it might not be able to satifsfy the second condition.
To learn more https://en.wikipedia.org/wiki/Monotone_cubic_interpolation
  4 个评论
显示 2更早的评论
Xinwei Li
Xinwei Li 2023-10-20
Hi Bruno,
Many thanks for your help. Now I get the idea of internally calculated derivatives, which is by imposing monotonicity.
Bruno Luong
Bruno Luong 2023-10-20
编辑：Bruno Luong 2023-10-20
"... which is by imposing monotonicity. "
Exactly

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Interpolation 的更多信息

标签

产品


版本

R2022a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by