[SciPy-user] Inexact Newton methods in scipy

[Nils Wagner]

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 ?


help (linalg.gmres) yields

   A --   An array or an object with a matvec(x) method
           to represent A * x

A small example illustrating an object with a matvec(x) method would be appreciated.


Nils