[SciPy-user] Inexact Newton methods in scipy

Pearu Peterson pearu at scipy.org
Fri Nov 12 06:40:31 CST 2004

On Fri, 12 Nov 2004, Nils Wagner wrote:

> Hi all,
> A standard method to solve nonlinear equations
> f(x) = 0
> is Newton's method. Given a suitable initial guess one iterates
> f'(x_k) \Delta x_k = -f(x_k)
> x_{k+1} = x_k + \Delta x_k
> If the Jacobian is not available in a direct manner, we can apply f'(x_k) to 
> a vector \Delta x_k by a finite difference formula (see my previous mail fdf 
> package)
> BTW, most publications deal with real Jacobians. How can I extend finite
> difference formulas to complex Jacobians ?

Apply finite difference formula to real and imaginary part of f(x) to get 
an approximation for complex Jacobian.


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