Hi Rene,

You want Interpolation rather than ListInterpolation. And notice that the argument is a list of {x1,x2, . . . y}.

 eqs = {
d   s=  =R=a ntd*osm R+e atl*[ {+ t*,b   1,0
,   a =={t*1c0 +0 t0
,   a =={t*1c0 +0 t0, 3  b]; == t*d + t*
,   a =={t*1c0 +0 t0, 3  b]; == t*d + t*f,
  c == t*s + t,
  d == t*s + t*a,
  f == t*c,
  e =f= t* d}=; 
nt e FullSoimlplaifty@iFiorsnt@[odve[eq;s, 
nt e FullSoimlplaifty@iFiorsnt@[odve[eq;s, {a, b, c,I ndt,e rep,o lfa, iosn}:,: uRdeegl:s ]I n/t/e rp
ati o n   oCno lunmsnt r/u/c tTurraeddi tgiroindasl Fiosr mc
rrently o
nly supported for InterpolationOrder->1 or InterpolationOrder->All. Order will be reduced to 1. >>

Plot3D[f[x, y], {x, 0, 10}, {y, 0, 10}]

InterpolatingFunction::dmval: Input value {0.000715,0.000715} lies outside the range of data in the interpolating function. Extrapolation will be used. >>

Hello Rene,

I'm very happy you had success! However, I'm very puzzled as to why my suggestion worked at all, if it did not identify (near) duplicate samples. Oh well, onward! :-)

At the bottom of (nearly) each page you have a 'see also' section, which also shows Interpolation in this case. Also at the very the top, on the right, you have a button Tutorials which shows: tutorial/ApproximateFunctionsAndInterpolation Which explains at length how interpolation can be done in Mathematica.

David,

I just tried to use this (my data set is humongously large with about 800,000 {x,y,f} elements) and Interpolation gives me the following set of discouraging reactions: 1. Interpolation::udeg: Interpolation on unstructured grids is currently only supported for InterpolationOrder->1 or InterpolationOrder->All. Order will be reduced to 1. >> 2. Interpolation::femimq: The element mesh has insufficient quality of -1.27917*10^-26. A quality estimate below 0. may be caused by a wrong ordering of element incidents or self-intersecting elements. >> 3. Interpolation::fememtlq: The quality -1.27917*10^-26 of the underlying mesh is too low. The quality needs to be larger than 0.`. >>

I tried doing some reordering of my original data set but also this reordered set didn't work and gave the same comments.

Do you have any idea what's going wrong and what I can do to break this deadlock?

René

Hi David,

This solves my problem indeed. You saved my day. Thanks a heap.

Two remarks, if I may: 1. I saw that both the list format {x1,x2, . . . y} as well as {{x1,x2, . . }, y} work in this case. (The Mathematica documentation recommends the latter format). 2. I would find it user-friendly if the Mathematica documentation for ListInterpolation would give am explicit referral to Interpolation for the case of non-grid lists. That would save other users a lot of heart ache.

Thanks so much for your advice, René