Iteration
Author: Nils Löhr, Stud., Prof. Dr. Dörte Haftendorn

Interaktive Umsetzung zum Aufgabenblatt

Tangente

Fixpunkt f(x)

Strecke A - F(x)

f(fX))

f(x)

Strecke A - f(f(x))

Tangente f(f(x))

Fixpunkte f(f(x))

Scheitelpunkt f(x)

Senkrechte

1

2

f(x)= -a (x-2)^2 +4

g(x) = x
a = 0.57 (slider from -5 to 5, step 0.0050)
f(x) = -1.0 * a * (x - 2.0)^(2.0) + 4.0
D, E = Intersect(f, g)
b = -3
n = 3 (slider from 0 to 200, step 1)
A = Point(xAxis)
x0: x(A)
L1 = IterationList(f, x0, n)
L3 = Sequence(Segment[(Element[L1, i], Element[L1, i + 1.0]), (Element[L1, i + 1.0], Element[L1, i + 1.0])], i, 1.0, n - 1.0)
L4 = Sequence(Segment[(Element[L1, i + 1.0], Element[L1, i + 1.0]), (Element[L1, i + 1.0], Element[L1, i + 2.0])], i, 1.0, n - 1.0)
y_A = Segment((x0, 0.0), (x0, f(x0)))
ntes = Element(L1, n + 1.0)
i = Tangent(E, f)
m = Slope(i)
a_1 = false
S = Extremum(f(x))
l = false
p = true
s(x) = f(f(x))
h = false
e = Segment((x0, 0.0), (x0, f(f(x0))))
q = true
L2 = IterationList(f(f(x)), x0, n)
B, C, F, G = Intersect(s, g)
r = Tangent(G, s)
t = Tangent(C, s)
m_1 = Slope(t)
m_2 = Slope(r)
list1 = Sequence(Segment[(Element[L2, r + 1.0], Element[L2, r + 1.0]), (Element[L2, r + 1.0], Element[L2, r + 2.0])], r, 1.0, n - 1.0)
list2 = Sequence(Segment[(Element[L2, r], Element[L2, r + 1.0]), (Element[L2, r + 1.0], Element[L2, r + 1.0])], r, 1.0, n - 1.0)
u = false
v = false
w = false
b_1 = OrthogonalLine(S, xAxis)
c_1 = OrthogonalLine(S, yAxis)
H = Intersect(c_1, yAxis)
I = Intersect(xAxis, b_1)
d_1 = Segment(H, S)
e_1 = Segment(S, I)
c = false
J = Point(g)
K = Point(xAxis)
L = Point(g)
d = Line(K, L)
j = OrthogonalLine(J, d)
k = false
o = true
z = false