Newton-Trägerfunktion
Author: Prof. Dr. Dörte Haftendorn
Date: 06+15 Juli 2013

Ha 06/2013

y_0

g(x)=x-\frac{f(x)}{f'(x)}

f'(x_0)=\frac{y_0}{x_0-x_1}

f(x) = exp(x) - (4 * x)
fs(x) = f'(x)
g(x) = x - f(x) / f'(x)
h(x) = x
X_0 = Point(xAxis)
T_0: (x(X_0), g(x(X_0)))
W_1: (g(x(X_0)), g(x(X_0)))
T_1: (x(W_1), g(x(W_1)))
W_2: (g(x(T_1)), g(x(T_1)))
T_2: (x(W_2), g(x(W_2)))
W_3: (g(x(T_2)), g(x(T_2)))
x_1 = Segment(X_0, T_0)
d_1 = Segment(T_0, W_1)
e_1 = Segment(W_1, T_1)
d_2 = Segment(T_1, W_2)
e_2 = Segment(W_2, T_2)
d_3 = Segment(T_2, W_3)
X_1: (g(x(X_0)), 0)
Y_0: (x(X_0), f(x(X_0)))
t_1 = Segment(Y_0, X_1)
Y_1: (x(X_1), f(x(X_1)))
X_2: (g(x(X_1)), 0)
t_2 = Segment(Y_1, X_2)
Y_2: (x(X_2), f(x(X_2)))
X_3: (g(x(X_2)), 0)
s_0 = Segment(X_0, Y_0)
s_1 = Segment(X_1, Y_1)
Y_3: (x(X_3), f(x(X_3)))
t_3 = Segment(Y_2, X_3)
s_2 = Segment(X_2, Y_2)
s_3 = Segment(X_3, Y_3)
X_4: (g(x(X_3)), 0)
t_4 = Segment(Y_3, X_4)
T_3: (x(W_3), g(x(W_3)))
W_4: (g(x(T_3)), g(x(T_3)))
e_3 = Segment(W_3, T_3)
d_4 = Segment(T_3, W_4)
x_4 = Segment(X_4, W_4)
A = Intersect(h, g, (2.1532923641103494, 2.1532923641103494))
B = Intersect(f, xAxis, (2.1532923634238603, -3.166890749639606E-9))
j = Segment(A, B)
Text1: "f(x)=" + (LaTeX[f]) + ""
d1, i, x_0, y_0 = Polygon(X_0, Y_0, X_1)
d2, y_1, x_2, k = Polygon(X_2, X_1, Y_1)
d3, y_2, x_3, l = Polygon(X_3, X_2, Y_2)
d4, y_3, m, n = Polygon(X_4, X_3, Y_3)