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Newton's method for nonlinear equations
We want to find the solution of the set of nonlinear
equations:

(13.31) 
The algorithm is the following:
 Choose
 Calculate a solution to the Newton equation:

(13.32) 

We use a linear model to derive the Newton step (rather than a
quadratical model as in unconstrained optimization) because the
linear model normally as a solution and yields an algorithm with
fast convergence properties (Newton's method has superlinear
convergence when the Jacobian is a continuous function and
local quadratical convergence when is Liptschitz continous).
Newton's method for unconstrained optimization can be derived by
applying Equation 13.32 to the set of nonlinear
equations
).
Frank Vanden Berghen
20040419