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I am trying to apply NSolve to an Interpolation function which I have evaluated before. For a function of 1 argument everything works out but as soon as I try to apply the procedure for a function of 2 arguments Mathematica throws an error message at me. Here is my code

t1 = ListInterpolation[Table[x^2 + y^2, {x, 0, 2, .1}, {y, 0, 2, .1}], {{0, 2}, {0, 2}}];

FindRoot[t1[x, x] == 1, {x, 1}]

NSolve[t1[x, x] == 1, x]

FindRoot works but for NSolve mathematica does not evaluate the interpolation function.

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Clear["Global`*"]

t1 = ListInterpolation[
   Table[x^2 + y^2, {x, 0, 2, .1}, {y, 0, 2, .1}],
   {{0, 2}, {0, 2}}];

For the case where both arguments are the same, define a single-argument function

f[x_?NumericQ] := t1[x, x]

NSolve[f[x] == 1, x]

enter image description here

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  • $\begingroup$ Thanks, it worked. Is there a possibility to store the InterpolationFunction in a kind of true function and work directly with it? $\endgroup$ – ricoschmidt_ber Sep 16 at 14:37
  • $\begingroup$ Look at NonlinearModelFit or related fitting functions. $\endgroup$ – Bob Hanlon Sep 16 at 14:42

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