* @brief Applies the accelerated `Fixed Point` method to find a root of a given mono-variable equation for given conditions.
* @brief Applies the accelerated `Fixed Point` method to find a root of a given mono-variable equation for given conditions.
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* This function will initialize the `MonoFunction` with the given `equation` & `der`, then perform the Accelerated `Fixed Point` method on it
* This function will initialize the `MonoFunction` with the given `equation` & `fixed-point equation`, then perform the Accelerated `Fixed Point` method on it
* for the given conditions (`max_iter`, `tolerance`, `start_point`), by instantiating the `Aitken` method with this `Fixed Point` class.
* for the given conditions (`max_iter`, `tolerance`, `start_point`), by instantiating the `Aitken` method with this `Fixed Point` class.
* It returns a `Solution` class which encapsulates all relevant & interesting information about the result of the method.
* It returns a `Solution` class which encapsulates all relevant & interesting information about the result of the method.
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* @param eq the equation of the `MonoFunction` we want to find a root of.
* @param eq the equation of the `MonoFunction` we want to find a root of.
* @param der the derivative of the `MonoFunction` we want to find a root of.
* @param fp the fixed-point equation `g(x)` such that `f(x) = g(x) - x`
* @param start_point the point from which the `Aitken` ( & `Fixed Point`) method will start to iterate.
* @param start_point the point from which the `Aitken` ( & `Fixed Point`) method will start to iterate.
* @param stop_tol the tolerance at which the `Aitken` method considers its sequence to be converged.
* @param stop_tol the tolerance at which the `Aitken` method considers its sequence to be converged.
* @param max_iter the maximal iterations the `Aitken` method will perform before returning, converged or not.
* @param max_iter the maximal iterations the `Aitken` method will perform before returning, converged or not.