maths.numerical_analysis.brent_method
=====================================

.. py:module:: maths.numerical_analysis.brent_method


Functions
---------

.. autoapisummary::

   maths.numerical_analysis.brent_method.brent_method


Module Contents
---------------

.. py:function:: brent_method(func: collections.abc.Callable[[float], float], left: float, right: float, tol: float = 1e-08, max_iter: int = 100) -> float

   Find the root of function func in the interval [left, right] using Brent's Method.

   Brent's Method combines bisection, secant, and inverse quadratic interpolation.


   Parameters
   ----------
   func : Callable[[float], float]
       Function for which to find the root.
   left : float
       Left endpoint of interval.
   right : float
       Right endpoint of interval.
   tol : float
       Tolerance for convergence (default 1e-8).
   max_iter : int
       Maximum number of iterations (default 100).


   Returns
   -------
   float
       Approximate root of func in [left, right].

   Raises
   ------
   ValueError
       If func(left) and func(right) do not have opposite signs.

   Examples
   --------
   >>> def f(x): return x**3 - x - 2
   >>> round(brent_method(f, 1, 2), 5)
   1.52138

   >>> def f2(x): return x**2 + 1
   >>> brent_method(f2, 0, 1)
   Traceback (most recent call last):
   ...
   ValueError: func(left) and func(right) must have opposite signs