Finding the roots of an equation using Newton-Raphson method but I don't know the equation!

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Hi all,
This is a challenging problem that I'm having difficulties with.
I've been given a P-code file (protected/hidden MATLAB code) that contains a function f function of two input variables 𝑥, 𝑦.
I'm to use my own my own coding of the Newton-Raphson to find all the roots of 𝑓, i.e. 𝑓(𝑥, 𝑦) = 0, given 𝑥, 𝑦 are real variables defined between [−5, 5]. Hint: The function roots are "special" points (unsure what is meant by that bit).
I have uploaded the P-code containing the unknown function here.
I can plot the function using the fsurf function:
And I can render the following plot:
Plot rendered when unknownFunction.p is used with fsurf
This shows me that it has four roots.
I have absolutely no idea where to go from here. Every iteration of Newton-Raphson requires me to work out the first derivate of 𝑓(𝑥, 𝑦) (so (𝑓'(𝑥, 𝑦) ) in order to progress which obviously I cannot do due to not knowing the original function.
Can anyone offer me some ideas or support? I'm also a complete novice at MATLAB so detail would be appreciated if possible.
Thank you.

Answers (1)

Jim Riggs
Jim Riggs on 26 Nov 2020
You use a numerical approximation for the derivative.
Start at some initial guess for x & y.
take a small step, and compute the change in the function value over deltax and delta y.
These are numerical estimates of df/dx and df/dy.

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