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Interpolation with known derivative values
*To*: mathgroup at smc.vnet.net
*Subject*: [mg119721] Interpolation with known derivative values
*From*: Mauro <msmscarlatti at googlemail.com>
*Date*: Sat, 18 Jun 2011 19:56:58 -0400 (EDT)
I need to interpolate the value of a function, given its exact values
and first derivatives at a set of points. I know how to do this with
Mathematica for polynomial interpolation - for example:
InterpolatingPolynomial[{{-0.212, 0.00234, 0.10912}, {-0.013, 0.0062,
0.48837}}, -0.05]
where -0.0212 is the coordinate of the first point, 0.00234 is the
value of the function there, and 0.10912 is the value of the first
derivative there, and -0.05 is the coordinate of the point at which I
am interpolating.
My question is: how do I use the Mathematica "Interpolation" function
for this same set of values?
I have tried
Interpolation[{{-0.212, 0.00234, 0.10912}, {-0.013, 0.0062, 0.48837}},
-0.05, Method -> "Spline"]
but I get the error "Interpolation::indim: The coordinates do not lie
on a structured tensor product grid."
Thanks.
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