621.sagews

def secant_find_root(func, x0, x1, num_iterations=10, full_output=True):
    """
    Use Secant method to find a root of ``func`` with initial guesses x0, and x1
    where ``func`` is a function in one variable.
    """  

    x0 = float(x0)   
    x1 = float(x1)
    for i in range (num_iterations):
        x2 = x1 - (f(x1)*(x1-x0))/(f(x1) - f(x0))        
        x1, x0 = x2, x1
        if full_output == True:
            print float(x2)
    return x2

f(x) = x^2 - 2
secant_find_root(f,10, 5)

3.46666666667 2.28346456693 1.72448420668 1.48150560738 1.42072598049 1.41436456133 1.41421390923 1.41421356239 1.41421356237 1.41421356237 1.41421356237310