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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