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