python实现迭代法求方程组的根过程解析

import numpy as np
import matplotlib.pyplot as plt
 
A = np.array([[8, -3, 2], [4, 11, -1], [6, 3, 12]])
b = np.array([[20, 33, 36]])
 
# 方法一：消元法求解方程组的解
result = np.linalg.solve(A, b.T)
print('Result:\n', result)
 
# 方法二：迭代法求解方程组的解
B = np.array([[0, 3/8, -2/8], [-4/11, 0, 1/11], [-6/12, -3/12, 0]])
f = np.array([[20/8, 33/11, 36/12]])
error = 1.0e-6
steps = 100
xk = np.zeros((3, 1)) # initialize parameter setting
errorlist = []
for k in range(steps):
  xk_1 = xk
  xk = np.matmul(B, xk) + f.T
  print('xk:\n', xk)
  errorlist.append(np.linalg.norm(xk-xk_1))
  if errorlist[-1] < error:
    print('iteration: ', k+1)
    break
 
# 把误差画出来
x_axis = [i for i in range(len(errorlist))]
plt.figure()
plt.plot(x_axis, errorlist)