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We want to find the solution of the set of non-linear
Newton's method for non-linear equations
The algorithm is the following:
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
- Calculate a solution to the Newton equation:
Frank Vanden Berghen