Line search.sagews

def dichotomous_search(f, a1, b1, eps, Delta):
    a = a1
    b = b1
    while b - a > eps:
        l = (a+b)/2 - Delta
        r = (a+b)/2 + Delta
        if f(l) <= f(r):
            b = r
        else:
            a = l
    return (a+b)/2

def golden_section(f, a1, b1, ell):
    alpha = 0.61803398874989
    a = a1
    b = b1
    l = a + (1 - alpha)*(b - a)
    r = a + alpha*(b - a)
    fl = f(l)
    fr = f(r)
    while b - a > ell:
        if fl > fr:
            a = l
            l = r
            r = a + alpha*(b - a)
            fl = fr
            fr = f(r)
        else:
            b = r
            r = l
            l = a + (1 - alpha)*(b - a)
            fr = fl
            fl = f(l)

    return (a+b)/2

def newtons_method(f, start, eps):
    fp = f.derivative()
    fpp = fp.derivative()
    x = start
    finished = false
    while not finished:
        newx = x - fp(x) / fpp(x)
        if (abs(newx - x) < eps) or (abs(fp(x)) < eps):
            finished = true
        x = newx
    return x

g(x) = x^4 - 3*x^3 + 2*x^2

plot(g, -1,2)

dichotomous_search(g, 1, 2, 1e-4, 1e-5)

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute flags=compile_flags), namespace, locals) File "", line 1, in <module> NameError: name 'dichotomous_search' is not defined

newtons_method(g, 1.3, 1e-6)

1.64038820320221

newtons_method(g, 0.8, 1e-6)

0.609611796797793

golden_section(g, 1, 2, 1e-4)

1.64040730584972