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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


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