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

์กฐํ ์: 10(์ต๊ทผ 30์ผ)
qwerty3 2020๋ 11์ 26์ผ
๋๊ธ: Jim Riggs 2020๋ 11์ 27์ผ
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 ๐ฅ, ๐ฆ.
I'm to use my own my own coding of the Newton-Raphson to find all the roots of ๐, i.e. ๐(๐ฅ, ๐ฆ) = 0, given ๐ฅ, ๐ฆ are real variables defined between [โ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:
fsurf(@unknownFunction)
And I can render the following plot:
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 ๐(๐ฅ, ๐ฆ) (so (๐'(๐ฅ, ๐ฆ) ) 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.
##### ๋๊ธ ์: 0ํ์์จ๊ธฐ๊ธฐ ์ด์  ๋๊ธ ์: -1

๋๊ธ์ ๋ฌ๋ ค๋ฉด ๋ก๊ทธ์ธํ์ญ์์ค.

### ๋ต๋ณ(1๊ฐ)

Jim Riggs 2020๋ 11์ 26์ผ
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.
##### ๋๊ธ ์: 7ํ์์จ๊ธฐ๊ธฐ ์ด์  ๋๊ธ ์: 6
Jim Riggs 2020๋ 11์ 27์ผ
Yes, separating out dx and dy is probably more correct.

๋๊ธ์ ๋ฌ๋ ค๋ฉด ๋ก๊ทธ์ธํ์ญ์์ค.

R2020b

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