# Find specific point in unknown "function"

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Peter Uwsen on 29 Mar 2019
Commented: Peter Uwsen on 29 Mar 2019
Hello,
I have the following problem:
I do know the "shape" of the relationship between two variables x and y, but I don't know the exact values and it takes a lot of time to calculate them.. (for each x I can find an y)
I'm interested in finding the point, where y=1. To get there I want to have to calculate as few values as possible.
Does anyone know an algorithm, that could help me do this and is more "efficient" than just increeasing gradualy x from x_start till I get the desired y?
PS: here you can see the genmeral shape of the relationship:
Jan on 29 Mar 2019
@Torsten: I'd vote for your solution, if it is posted as answer.

Alan Weiss on 29 Mar 2019
Edited: Alan Weiss on 29 Mar 2019
The most efficient way is to use fzero as Torsten said. Your function is @(x)y(x)-1. For the most efficiency, set the initial point x0 to an interval [x1,x2] where the function changes sign between x1 and x2.
Alan Weiss
MATLAB mathematical toolbox documentation
P.S. If you have Optimization Toolbox, then fsolve can be even faster than fzero.
Peter Uwsen on 29 Mar 2019
Ok cool!
Thanks for the quick answers :)