I'm looking for a good vector transfer function...

I've got sets of data from 2 sources. Both have the same number of points in the x-axis but the 2 sets are different and the changes vary across the range. For example at one end there may be a 2 point difference, at the early end it may be 10 points and differences in between may be non-linear. I'd like to calculate a transfer function and then apply it to the new set of data to make it better match the original set. All I have to calculate the transfer function is one vector from the original and one from the new system (parent/child). The vectors have broad features, not a lot of fine peaks, and my goal is to end up with a minimal difference between the original and the transferred new vector. I've tried some options with varied success, and am guessing that this need is pretty common and there are probably some algorithms optimized for this. Any suggestions (including from existing toolboxes) greatly appreciated.