Adaptive FunctionInterpolation[] ?
- To: mathgroup at smc.vnet.net
- Subject: [mg33223] Adaptive FunctionInterpolation[] ?
- From: franki at aerodyne.com (Frank J. Iannarilli, Jr.)
- Date: Sat, 9 Mar 2002 03:20:06 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hi, 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[] package. So this is a cry to WRI or anyone who may already have the goods to come forward with this capability...it'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 possible). Regards, Frank J. Iannarilli +++++++++++++ Back in 1999, Carl Woll wrote: I am trying to use FunctionInterpolation to approximate a function <snip> (given the default option InterpolationPoints -> 11 ...) In investigating 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 finer 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 region 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. This is apparently not so. Is this really true, or is there a way to force FunctionInterpolation to select points adaptively. If not, what does the option MaxRecursion do? -- Carl Woll Dept of Physics U of Washington