Function example_solution_newton

main.py:214–246

Run an example 'Solutions: Newton'.

()

@print_docstring
def example_solution_newton():
    """Run an example 'Solutions: Newton'."""
    # Newton method (find roots of an equation)
    #   Pros:
    #       It is a fast method.
    #    Cons:
    #       It may diverge;
    #       It is necessary to calculate the derivative of the function;
    #       It is necessary to give an initial x0 value where
    #           f'(x0) must be nonzero.

    def f(x):
        return 2 * x ** 3 - math.cos(x + 1) - 3

    def df(x):
        return 12 * x ** 2 + 1 - math.sin(x)

    x0 = 1.0
    toler = 0.01
    iter_max = 100

    print("Inputs:")
    print(f"x0 = {x0}")
    print(f"toler = {toler}")
    print(f"iter_max = {iter_max}")

    print("Execution:")
    root, i, converged = solutions.newton(f, df, x0, toler, iter_max)

    print("Output:")
    print(f"root = {root:.5f}")
    print(f"i = {i}")
    print(f"converged = {converged}")


@print_docstring