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feat: aufgabe 4 abgeschlossen

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git-sandro 2026-02-26 23:09:06 +01:00
parent fe8866f1df
commit b0f13399bb
1 changed files with 29 additions and 15 deletions
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44
introduction/serie_2.py
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@ -4,32 +4,46 @@ import numpy as np
# %%
print("Aufgabe 4")
def fixpunkt_iteration(f, x, tol=1e-7):
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]
x0 = 1.0
f = lambda x: 1-(1/5)*x
fixpunkt_a, iterationen_a = fixpunkt_iteration(f, x0)
f = np.cos
fixpunkt_b, iterationen_b = fixpunkt_iteration(f, x0)
f = lambda x: np.e**-x
fixpunkt_c, iterationen_c = fixpunkt_iteration(f, x0)
# Ausgabe
print("----------------------------------------------------------------------")
print(__file__)
print("----------------------------------------------------------------------")
print(f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n")
print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")
print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
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("----------------------------------------------------------------------")