.. _glossary:

Glossary
========


Technical terms used in the lab assignment material.

.. glossary::

    Newton-Raphson method
        (also known as Newton's method) is an algorithm to **find the
        root** of a function (i.e. find :math:`x` such that :math:`f(x)=0`).
        In particular, it is a popular method to solve the AC power flow equations
        (default method in MATPOWER, see §4.1 of the manual [MATPOWER-man]_).
        
        It proceeds in an iterative manner, starting from an initial
        guess :math:`x_0` (provided by the user).
        This guess is refined with a linear approximation of the function,
        using the knowledge of the gradient :math:`f'(x)`)
        
        .. math::
        
            x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}

        see e.g. Wikipedia for a graphical animation of the method in 1D
        https://en.wikipedia.org/wiki/Newton's_method