numerical_methods.roots package

Submodules

numerical_methods.roots.dichotomie module

numerical_methods.roots.dichotomie.dichotomy(start, end, tolerance, func, verbose=True)[source]

Bisection method to find a root of a continuous function in [start, end].

Parameters:

  • start (float) – Lower bound of the interval.

  • end (float) – Upper bound of the interval.

  • tolerance (float) – Accepted error margin for the root.

  • func (callable) – Continuous function f(x) such that f(start) * f(end) < 0.

  • verbose (bool) – If True, prints each iteration step.

Returns:

Approximate root and list of iterations (a, b, midpoint).

Return type:

tuple[float, list[tuple[float, float, float]]]

Raises:

ValueError – If f(start) * f(end) >= 0.

numerical_methods.roots.newton module

numerical_methods.roots.newton.newton(tolerance, func, func_derivative, initial_guess=1.0, max_iterations=1000, verbose=True)[source]

Newton-Raphson method to find a root of a function.

Parameters:

  • tolerance (float) – Accepted error margin.

  • func (callable) – Function f(x).

  • func_derivative (callable) – Derivative f’(x).

  • initial_guess (float) – Starting value.

  • max_iterations (int) – Maximum number of iterations.

  • verbose (bool) – If True, prints each iteration step.

Returns:

Approximate root and list of iterations (i, x0, x).

Return type:

tuple[float, list[tuple[int, float, float]]]

Raises:

  • ZeroDivisionError – If f’(x) = 0 during an iteration.

  • RuntimeError – If the max number of iterations is reached.

numerical_methods.roots.point_fixe module

numerical_methods.roots.point_fixe.fixed_point(tolerance, g_func, initial_guess=1.0, max_iterations=1000, verbose=True)[source]

Fixed-point iteration method to find a solution of x = g(x).

Parameters:

  • tolerance (float) – Accepted error margin.

  • g_func (callable) – Function g(x) such that x = g(x).

  • initial_guess (float) – Starting value.

  • max_iterations (int) – Maximum number of iterations.

  • verbose (bool) – If True, prints each iteration step.

Returns:

Approximate fixed point and list of iterations (i, x0, x).

Return type:

tuple[float, list[tuple[int, float, float]]]

Raises:

RuntimeError – If the max number of iterations is reached.

Module contents