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Given this system of nonlinear equations, solve them by fixed-point iteration starting from $(1,-1,1)$: $$\begin{align} 9xy+y^2+3z+18&=0\tag1\\ x^2+12xy-yz+33&=0\tag2\\ 5x-4yz+z^2-26&=0\tag3\end{align}$$

How can I choose $3$ functions $f, g, h$ satisfying ,$ x=f(x,y,z), \ y=g(x,y,z) \ and \ z=h(x,y,z). $

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    yes , you are right ,in the 3rd equation power of z is 2 – 2017-02-02
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    any help is appreciating – 2017-02-02
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    partial derivatives with respect to x, y,z – 2017-02-02
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    For your first function, I take$ |\partial f_{1x} \times f(1,-1,1)| + |\partial f_{1y} \times f(1,-1,1)| + |\partial f_{1z} \times f(1,-1,1)| $and it is greater than $1$. Can you provide more details of how you did it? – 2017-02-02
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    yes you are absolutely right, my calculation was wrong, so any other way can i solve the problem with different choice ? can you you suggest f1,f2,f3 – 2017-02-02
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    yes it is to be solved by fixed point iteration – 2017-02-02
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    i am not sure, but it was given to me as question to solve – 2017-02-02

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