Interpolate between two data sets

Dear Root-Users

I have two data sets, describing measurements at different energies, each data set contains a length(position) and an arbitrary value (of interest). The number of data points within these sets can be different (different positions as well).

I want to interpolate values at an energy in between these two.
To use the Interpolator function I would basically need to create a third data set at this energy.

What I found so far: I could implement it in the following way:
Use Interpolator class to interpolate data set A to get a fixed number of data points at the same position as in data set B, do the same with data set B. Now call the Interpolator for every data point in A and B to get the new data set.
This sounds quite inefficient to me. Is there a better way to do that?

Example (I just made up the values, no real interpolation was done)
length value
0.15 23
0.25 26
0.35 43
0.45 44
0.55 50

length value
0.17 24
0.27 27
0.37 44
0.57 52

length value
0.1 20
0.28 24
0.3 41
0.448 42
0.51 48

Any help would be greatly appreciated.