50 lines
1.3 KiB
Python
50 lines
1.3 KiB
Python
#%%
|
|
import numpy as np
|
|
|
|
# %%
|
|
print("Aufgabe 4")
|
|
|
|
def fixpunkt_iteration(f, x=1.0, tol=1e-7, N=1000):
|
|
x_new = f(x)
|
|
i = 0
|
|
|
|
while(np.abs(x_new-x) > tol):
|
|
if i > N:
|
|
raise RuntimeError("Keine Konvergenz erreicht")
|
|
|
|
x = x_new
|
|
x_new = f(x)
|
|
i += 1
|
|
return [x_new, i]
|
|
|
|
# Ausgabe
|
|
print("----------------------------------------------------------------------")
|
|
print(__file__)
|
|
print("----------------------------------------------------------------------")
|
|
|
|
f = lambda x: 1-(1/5)*x
|
|
try:
|
|
fixpunkt_a, iterationen_a = fixpunkt_iteration(f)
|
|
except RuntimeError as error:
|
|
print(f"a) f(x) = 1-(1/5)*x\n{error}")
|
|
else:
|
|
print(f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n")
|
|
|
|
f = np.cos
|
|
try:
|
|
fixpunkt_b, iterationen_b = fixpunkt_iteration(f)
|
|
except RuntimeError as error:
|
|
print(f"b) f(x) = cos(x)\n{error}")
|
|
else:
|
|
print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")
|
|
|
|
f = lambda x: np.e**-x
|
|
try:
|
|
fixpunkt_c, iterationen_c = fixpunkt_iteration(f)
|
|
except RuntimeError as error:
|
|
print(f"c) f(x) = e⁻x\n{error}")
|
|
else:
|
|
print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
|
|
|
|
print("----------------------------------------------------------------------")
|