[gmx-users] cubic spline and continuous derivatives

[Berk Hess]

Hi,

Yes.
Cubic spline interpolation means piecewise interpolation with third order polynomials.
The terms says nothing about which derivatives are continuous.

Cubic spline interpolation is often used to interpolate between points where only
the function value itself is provided and in that case one usually chooses to match
the second derivative at the reference points. But that is just one of the many uses
of cubic spline interpolation.

Berk

> Date: Sun, 19 Sep 2010 01:32:44 -0700
> From: floris_buelens at yahoo.com
> To: gmx-users at gromacs.org
> Subject: [gmx-users] cubic spline and continuous derivatives
> 
> Hello,
> 
> The gromacs manual states that for cubic spline interpolation of potential 
> energy and forces, "V and V’ are continuous, while V” is the first discontinuous 
> derivative." This makes sense to me as there is a unique solution for parameters 
> A2 and A3 if V and V' to the left and right are given for each piecewise 
> polynomial.
> However the definition of a cubic spline seems to be for a set of functions 
> continous up to the second derivative. Is the cubic spline formulation used 
> somehow unorthodox in this sense? I'm using a similar scheme in a slightly 
> different context, is it strictly correct to refer to it as cubic spline 
> interpolation?
> Thanks,
> 
> Floris
> 
> 
>       
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