def fd1(x):
    return 1+1/x**2

def fd2(x):
    return 1/(x-1)**0.5

# 迭代法求解方程
def Renew(x,fd,err):
    count=0
    i = 0
    try:
        while True:
            xk = fd(x)
            print(f"当前迭代值: {xk}, 上一次迭代值: {x}, 误差: {abs(xk-x)}")
            if abs(i) < (xk-x):
                count += 1
            else:
                count = 0
            if count > 10:
                print("不收敛")
                break
            if abs(xk-x) < err:
                return xk
            i = xk-x
            x = xk
    except Exception as e:
        print(f"发生错误: {e}")
        return None
    return None


# 定义迭代公式 x = fd(x)  ###############################
def fd(x):
    return 1+1/x**2

if __name__ == "__main__":
    ##############################################################################################################
    x0 = 1.5         # 初始值
    err = 1e-5        # 精度要求          P136

    result = Renew(x0, fd, err)
    if result is not None:
        print(f"收敛 解为: {result:.5f}")
    else:
        print("不收敛")