Find specific point in unknown "function"

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?

Thanks in advance!

PS: here you can see the genmeral shape of the relationship:

[Torsten]

Solve y(x) - 1 = 0 using Newton's method (e.g. with the help of MATLAB's fsolve).

[KSSV]

interp1....

[Jan]

@Torsten: I'd vote for your solution, if it is posted as answer.

Answer 1

[Alan Weiss]

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]

Ok cool!

Thanks for the quick answers :)