simultaneous and constrained interpolation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg112906] simultaneous and constrained interpolation?*From*: dantimatter <google at dantimatter.com>*Date*: Tue, 5 Oct 2010 05:36:19 -0400 (EDT)

Hello All, I'm back with another interpolation-related question: is it possible to interpolate between two sets of points in such a way so that the average of the two interpolation functions lies along a known curve? Put another way, I have a set of points {a1, a2, ..., aN} that I know is actually the average of two other unknown sets of points (a1=(b1+c1)/2, a2=(b2+c2)/2, ...). Now I don't know what most of the b's and c's are, but I do know the endpoints b1, bN and c1, cN and can interpolate between them. Is there a way to simultaneously interpolate to get all the b's and c's while enforcing that their average be equal to the a's? Thanks! dan