[gmx-users] cubic spline and continuous derivatives
Floris Buelens
floris_buelens at yahoo.com
Sun Sep 19 10:32:44 CEST 2010
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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