Using Reduce with a Interpolation function

Asked Jun 19 '20 at 02:24

Active Jul 09 '20 at 12:20

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I am trying to find all the solutions of an equation that contains an interpolation function int, where int=Interpolation[data] (the interpolation of some data I have).

When I tried to use Reduce such as:

Reduce[int''[x] == 0, {x}]

I get an error saying "Reduce::inex: Reduce was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Reduce require exact input, providing Reduce with an exact version of the system may help.".

The same is true if I use NSolve as NSolve[int''[x] == 0, x]

Question: How can I use Reduce when my input is an interpolation function?

edited Jul 09 '20 at 12:20

J. M.'s missing motivation

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asked Jun 19 '20 at 02:24

John

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AFAIK, Reduce won't work with interpolated functions. NSolve should work like you said, so without seeing the data I can't say why it didn't work. NSolve will likely only return a subset of the solutions. FindRoot can be used to find all solutions, but you need to know where they are, roughly. See this question on finding all of them automatically. – imas145 Jun 19 '20 at 07:01
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Try converting the interpolating function to a Piecewise polynomial. – Michael E2 Jun 19 '20 at 23:35
@MichaelE2 thanks! thats a good idea ! – John Jun 20 '20 at 00:30
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Apart from converting your interpolant to a piecewise function, you could also use the MeshFunctions option of Plot[], or use NDSolve[] with WhenEvent[] to seek roots. – J. M.'s missing motivation Jul 09 '20 at 12:22

Using Reduce with a Interpolation function

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