25 lines
655 B
Python
25 lines
655 B
Python
import numpy as np
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A = np.array([[8, 5, 2], [5, 9, 1], [4, 2, 7]], dtype=float)
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b = np.array([19, 5, 34], dtype=float)
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x_k = np.array([1, -1, 3], dtype=float)
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U = np.triu(A, 1)
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DL = np.tril(A)
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DL_inv = np.linalg.inv(DL)
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print(f"Startvektor x(0): {np.around(x_k, 4)}")
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x_history = [x_k.copy()]
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for k in range(1, 4):
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x_new = np.dot(DL_inv, (b - np.dot(U, x_k)))
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x_history.append(x_new.copy())
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x_k = x_new
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print(f"x({k}): {np.around(x_k, 4)}")
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x_1 = np.array([2.7500, -1.4167, 3.5714])
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x_2 = np.array([2.1190, -1.0873, 3.9780])
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x_3 = np.array([1.9861, -0.9945, 4.0049])
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print("-" * 35)
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print(f"Näherung x(3) (4 Dezimalstellen): {x_3}") |