Help required to solve a system of non-linear Eq.,s

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2 total messages Started by Pattalachinti Wed, 18 Nov 1992 02:44

#856

Author: Pattalachinti
Date: Wed, 18 Nov 1992 02:44

9 lines
758 bytes

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

Re: Help required to solve a system of non-linear Eq.,s

#871

Author: samer Takriti
Date: Wed, 18 Nov 1992 17:48

19 lines
1191 bytes

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

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