620.sagews

def method_of_false_position_find_root(f, a, b, num_iterations=10, full_output=True):
    """
    Use Method of False Position to find a root of ``f`` on the closed interval `[a,b]`
    (or `[b,a]`) if possible, where ``f`` is a function in the one variable.
    page 67 of Timothy Sauer's Numerical Analysis text
    """  

    #convert to floats
    a = float(a); b = float(b)
    if a > b:
        a, b = b, a
    
    for i in range (num_iterations):
        c = (f(b)*a - f(a)*b)/(f(b) - f(a))
        if f(a)*f(c) < 0:
            b=c
        else:
            a=c
        if full_output == True:
            print float(c)
    
    return c

f(x) = x^2 - 2
method_of_false_position_find_root(f, 0, 10,20)

0.2 0.392156862745 0.569811320755 0.728311317387 0.865291181364 0.98045341223 1.07504978885 1.15128131535 1.21177224136 1.25918740674 1.29599708578 1.32436036803 1.34608959667 1.36266295405 1.3752612045 1.38481321543 1.39204147266 1.39750322756 1.40162559788 1.40473442504 1.40473442503999