🚀 go-pugleaf

In article <1992Nov18.024417.19684@oucsace.cs.ohiou.edu> ravi@bobcat.ent.ohiou.edu (Pattalachinti) writes:
>Are there any thumb-rules for the successful execution of
>Newton-Raphson method to work successfully on a non-linear
>system of equations.
>
>Any suggestion is welcome,
>
>Thanking in advance,
>
>Ravi 

I think that what you are looking for is "Kantarovitch theorem". It states
that if the function is continuously differentiable, the norm of the e
inverse of the Jacobian is less than beta, and the norm of the (J^{-1}F(x))
is less than eta (J is the jacobian) then
if alpha * beta * eta <= .5 then the sequence converges.
F is lipschitz continuous with constant alpha.
-Samer