Editing Secant method (section)

==Computational example==
Below, the secant method is implemented in the [[Python (programming language)|Python]] programming language. 

It is then applied to find a root of the function {{math|''f''(''x'') {{=}} ''x''<sup>2</sup> − 612}} with initial points <math>x_0 = 10</math> and <math>x_1 = 30</math>

<syntaxhighlight lang="python3">
def secant_method(f, x0: int, x1: int, iterations: int) -> float:
    """Return the root calculated using the secant method."""
    for i in range(iterations):
        x2 = x1 - f(x1) * (x1 - x0) / float(f(x1) - f(x0))
        x0, x1 = x1, x2
        # Apply a stopping criterion here (see below)
    return x2

def f_example(x):
    return x ** 2 - 612

root = secant_method(f_example, 10, 30, 5)

print(f"Root: {root}")  # Root: 24.738633748750722

</syntaxhighlight>

It is very important to have a good stopping criterion above, otherwise, due to limited numerical precision of floating point numbers, the algorithm can return inaccurate results if running for too many iterations. For example, the loop above can stop when one of these is reached first: {{Mono|abs(x0 - x1) < tol}}, or {{Mono|abs(x0/x1-1) < tol}}, or {{Mono|abs(f(x1)) < tol}}. <ref>{{cite web | url=https://www.cfm.brown.edu/people/dobrush/am33/Matlab/ch3/secant.html | title=MATLAB Tutorial for the First Course. Part 1.3: Secant Methods }}</ref>