Berikut saya sapaikan metode Jacobi dan Metode Gauss-Seidel untuk menyelesaikan n persamaan, dengan n bilangan anu secara iteratif.
Metode Jacobi
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import numpy
as np # Define the matrix A and vector b A =
np.array([[5, -1, 1, 2], [2, 7, -1, -2], [2, -3, 8, 1], [7, -3, 1, 9]]) b =
np.array([-4, 3, 1, 12]) # Solve the system of equations A*x = b xx =
np.linalg.solve(A, b) # Print the solution print("xx
=") print(xx) # Iterative process n = 4 w, x, y, z =
0, 0, 0, 0 print("\nIterative
refinement:") print("iter w1 x1 y1 z1") for i in
range(1, 21): w1 = (b[0] - (x*A[0,1]) - y*A[0,2] -
z*A[0,3]) / A[0,0] x1 = (b[1] - w*A[1,0] - y*A[1,2] -
z*A[1,3]) / A[1,1] y1 = (b[2] - w*A[2,0] - x*A[2,1] -
z*A[2,3]) / A[2,2] z1 = (b[3] - w*A[3,0] - x*A[3,1] -
y*A[3,2]) / A[3,3] print(f"{i:4d} {w1:10f} {x1:10f}
{y1:10f} {z1:10f}") # Check for convergence if np.abs(w1-w) < 0.0001 and
np.abs(x1-x) < 0.0001 and np.abs(y1-y) < 0.0001 and np.abs(z1-z) <
0.0001: break w, x, y, z = w1, x1, y1, z1 |
Metode Gauss-Seidel
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import numpy
as np # Define the matrix A and vector b A =
np.array([[5, -1, 1, 2], [2, 7, -1, -2], [2, -3, 8, 1], [7, -3, 1, 9]]) b =
np.array([-4, 3, 1, 12]) # Solve the system of equations A*x = b xx =
np.linalg.solve(A, b) print("xx
=") print(xx) # Initial guesses for the solution w = x = y = z
= 0 print("\nIterative process:") # Store the
iteration results table = [] for i in
range(1, 21): w_old, x_old, y_old, z_old = w, x, y,
z # Store old values for convergence
check w = (b[0] - (x*A[0,1]) - y*A[0,2] -
z*A[0,3]) / A[0,0] x = (b[1] - w*A[1,0] - y*A[1,2] -
z*A[1,3]) / A[1,1] y = (b[2] - w*A[2,0] - x*A[2,1] -
z*A[2,3]) / A[2,2] z = (b[3] - w*A[3,0] - x*A[3,1] -
y*A[3,2]) / A[3,3] # Save the iteration results table.append([i, w, x, y, z]) # Check for convergence if np.allclose([w_old, x_old, y_old,
z_old], [w, x, y, z], atol=0.0001): break # Print the
results print(" iter
w x y z") for row in
table: print(f"{row[0]:5d} {row[1]:10f}
{row[2]:10f} {row[3]:10f} {row[4]:10f}") |
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