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Adaptive FunctionInterpolation[] ?

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  • Subject: [mg33223] Adaptive FunctionInterpolation[] ?
  • From: franki at (Frank J. Iannarilli, Jr.)
  • Date: Sat, 9 Mar 2002 03:20:06 -0500 (EST)
  • Sender: owner-wri-mathgroup at


I too have experienced Carl Woll's finding (referenced below) that
FunctionInterpolation[] does NOT adaptively sample the underlying
(exact) function in determining its sampling grid.

Various related newsgroup postings have suggested manually combining
sets of InterpolationFunctions, each computed for a differing region
of the domain at appropriate (fixed) grid density.  But of course,
this is a pain, and not at all a general solution.  MathSource
apparently does not contain any adaptive FunctionInterpolation[]

So this is a cry to WRI or anyone who may already have the goods to
come forward with this's really a good-to-have in
furthering Mathematica's appeal.  I know one could craft it based
around ListInterpolation[], but I'm looking to save this effort (if


Frank J. Iannarilli


Back in 1999, Carl Woll wrote:
  I am trying to use FunctionInterpolation to approximate a function 


(given the default option InterpolationPoints -> 11 ...) In
the behavior of FunctionInterpolation, I discovered that it calculates
points on an 11x11 grid only. When I increase the number of
interpolation points, FunctionInterpolation calculates points on a
grid. However, there is only one region of space where the answer is
poor, so I only want to increase the number of points used in the
where the answer is poor, not everywhere. How can I do this?

Since FunctionInterpolation has a MaxRecursion option, I figured that
FunctionInterpolation used an adaptive procedure to select points.
is apparently not so. Is this really true, or is there a way to force
FunctionInterpolation to select points adaptively. If not, what does
option MaxRecursion do?

Carl Woll
Dept of Physics
U of Washington

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