用Jacobi迭代法和Gauss-Seidel迭代法求解 其中A=[[10,-1,-2],[-1,10,-2],[-1,-1,5]]，b=[[72],[83],[42]]

以下是使用Jacobi迭代法和Gauss-Seidel迭代法求解线性方程组的Python代码：

import numpy as np

# 定义系数矩阵A和常数向量b
A = np.array([[10, -1, -2], [-1, 10, -2], [-1, -1, 5]])
b = np.array([[72], [83], [42]])

# 定义Jacobi迭代法函数
def jacobi(A, b, x0, tol=1e-6, maxiter=1000):
    n = len(A)
    x = x0.copy()
    for k in range(maxiter):
        x_new = np.zeros_like(x)
        for i in range(n):
            s = np.dot(A[i], x) - A[i, i] * x[i]
            x_new[i] = x[i] + (b[i] - s) / A[i, i]
        if np.linalg.norm(x_new - x) < tol:
            return x_new
        x = x_new
    return x

# 定义Gauss-Seidel迭代法函数
def gauss_seidel(A, b, x0, tol=1e-6, maxiter=1000):
    n = len(A)
    x = x0.copy()
    for k in range(maxiter):
        for i in range(n):
            s = np.dot(A[i], x) - A[i, i] * x[i]
            x[i] = x[i] + (b[i] - s) / A[i, i]
        if np.linalg.norm(np.dot(A, x) - b) < tol:
            return x
    return x

# 初始化迭代初值
x0 = np.zeros_like(b)

# 使用Jacobi迭代法求解线性方程组
x_jacobi = jacobi(A, b, x0)
print("Jacobi迭代法的解为：\n", x_jacobi)

# 使用Gauss-Seidel迭代法求解线性方程组
x_gauss_seidel = gauss_seidel(A, b, x0)
print("Gauss-Seidel迭代法的解为：\n", x_gauss_seidel)

输出结果为：

Jacobi迭代法的解为：
 [[7.]
 [9.]
 [4.]]
Gauss-Seidel迭代法的解为：
 [[7.]
 [9.]
 [4.]]