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How do you calculate the intersection of discrete data points and an equation?

Actually I have two ways already, one is to just take the equation of the discrete points then solve it using a root-finding technique. The other would be substituting the x values of the discretized points to the equation, then comparing the y values of the discretized points and the calculated y values from the equation; they should be close (if not totally similar). While this method seems to work, it isn't... exactly possible in my situation.

Is there any other way to do this?

Actually I have two ways already, one is to just take the equation of the discrete points then solve it using a root-finding technique. The other would be substituting the x values of the discretized points to the equation, then comparing the y values of the discretized points and the calculated y values from the equation; they should be close (if not totally similar). While this method seems to work, it isn't... exactly possible in my situation.

Is there any other way to do this?

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