Function example_solution_secant

main.py:96–129

Run an example 'Solutions: Secant'.

()

@print_docstring
def example_solution_secant():
    """Run an example 'Solutions: Secant'."""
    # Secant method (find roots of an equation)
    #   Pros:
    #       It is a fast method (slower than Newton's method);
    #       It is based on the Newton method but does not need the derivative
    #           of the function.
    #   Cons:
    #       It may diverge if the function is not approximately linear in the
    #           range containing the root;
    #       It is necessary to give two points, 'a' and 'b' where
    #           f(a)-f(b) must be nonzero.

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

    a = -1.0
    b = 2.0
    toler = 0.01
    iter_max = 100

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

    print("Execution:")
    root, i, converged = solutions.secant(f, a, b, toler, iter_max)

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


@print_docstring