雅可比迭代、高斯-赛德尔迭代

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原创 2022-03-06 16:38:08 686 阅读 AI 写同款· GEO 优化 ›

分别用雅可比（Jacobi）迭代法和高斯—塞德尔（Gauss—Seidel）迭代法求解线性方程组 算法介绍（迭代法介绍）：代码C语言实现; # include # include # define N 6 /* *使用雅可比迭代法和高斯-赛德尔迭代法求解线性方程组 */ main(){ float NF2(float *x,float *y); float A[N][N],b[N],sum=0; float x[N],y[N]={0},x0[ 阅读详情

"""
求解线性方程组
    5*x_1 -   x_2 +   x_3 = 10
    2*x_1 - 8*x_2 -   x_3 = 11
    -x_1  +   x_2 + 4*x_3 = 3
初值为 x1 = x2 = x3 = 0
"""

"""雅可比迭代法"""
def jacobi_iteration():
    x1 = x2 = x3 = 0
    x1_next = (x2 - x3 + 10) / 5
    x2_next = (-2 * x1 + x3 + 11) / 8
    x3_next = (x1 - x2 + 3) / 4
    while abs(abs(x1) - abs(x1_next)) > 0.0001 or abs(abs(x2) - abs(x2_next)) > 0.0001 or abs(
            abs(x3) - abs(x3_next)) > 0.0001:
        x1 = x1_next
        x2 = x2_next
        x3 = x3_next
        x1_next = (x2 - x3 + 10) / 5
        x2_next = (-2 * x1 + x3 + 11) / 8
        x3_next = (x1 - x2 + 3) / 4
    print('x1:\n {0}  {1}'.format(x1, x1_next))
    print('x2:\n {0}  {1}'.format(x2, x2_next))
    print('x3:\n {0}  {1}\n'.format(x3, x3_next))


"""高斯-赛德尔迭代法"""
def Gauss_Seidel_iteration():
    x1 = x2 = x3 = 0
    x1_next = (x2 - x3 + 10) / 5
    x2_next = (-2 * x1_next + x3 + 11) / 8
    x3_next = (x1_next - x2_next + 3) / 4
    while abs(abs(x1) - abs(x1_next)) > 0.0001 or abs(abs(x2) - abs(x2_next)) > 0.0001 or abs(
            abs(x3) - abs(x3_next)) > 0.0001:
        x1 = x1_next
        x2 = x2_next
        x3 = x3_next
        x1_next = (x2 - x3 + 10) / 5
        x2_next = (-2 * x1_next + x3 + 11) / 8
        x3_next = (x1_next - x2_next + 3) / 4
    print('x1:\n {0}  {1}'.format(x1, x1_next))
    print('x2:\n {0}  {1}'.format(x2, x2_next))
    print('x3:\n {0}  {1}\n'.format(x3, x3_next))


if __name__ == '__main__':
    print('雅可比迭代法：')
    jacobi_iteration()

    print('高斯-赛德尔迭代法')
    Gauss_Seidel_iteration()