I am looking for a numerical method that can solve a system of non-linear equations. The non-linear

klamytewoc

klamytewoc

Answered question

2022-02-25

I am looking for a numerical method that can solve a system of non-linear equations. The non-linear equations are polynomials that are in one of the following forms:
c1x1+c2x2++cnxn=C
d1x12+d2x22++dnxn2=D
(The variables are x1,x2,xn.)
I can't get initial guesses that are close to the root. Is there a good numerical method to solve the system of equations?

Answer & Explanation

Hashim Townsend

Hashim Townsend

Beginner2022-02-26Added 5 answers

So if I understood your question correctly you are trying to solve a non-linear system of equations of the form
Ax+xTBx=b.
Restating it as
(A+xTB)x=b
x=(A+xTB)1b=f(x)
xf(x)=0
a fixed point is found. Any root-finding method can now be used. For example, the simplest approach would be a fixed-point iteration of the form
xi+1=(A+xiTB)1b
but alternatives include Newtons

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