实验代码

w = 3
b = 4
delta_z = 12
i = 0while abs( delta_z ) > 1e-5 :i = i + 1x = 2 * w + 3 * by = 2 * b + 1z = x * ydelta_z = z - 150.0factor_b = 3 * y + 2 * xfactor_w = 2 * ydelta_b = delta_z / ( 2 * factor_b )delta_w = delta_z / ( 2 * factor_w )b = b - delta_bw = w - delta_wprint("w = %f\t b = %f\t z = %f\t" % (w, b, z))print("delta_w = %f\t delta_b = %f\t delta_z = %f\t" % (delta_w, delta_b, delta_z))print("factor_w = %f\t factor_b = %f\t" % (factor_b, factor_w))print("---------------------------------------------------------------------------------------------")
print("result: 经过了%d次迭代，最终b = %f\tw = %f  此时精度为1e-5" % (i, b, w))

实验结果

每次迭代更新factor_b和factor_w的结果

w = 2.666667     b = 3.904762    z = 162.000000
delta_w = 0.333333   delta_b = 0.095238  delta_z = 12.000000
factor_w = 63.000000     factor_b = 18.000000
---------------------------------------------------------------------------------------------
w = 2.661519     b = 3.903263    z = 150.181406
delta_w = 0.005148   delta_b = 0.001499  delta_z = 0.181406
factor_w = 60.523810     factor_b = 17.619048
---------------------------------------------------------------------------------------------
w = 2.661517     b = 3.903263    z = 150.000044
delta_w = 0.000001   delta_b = 0.000000  delta_z = 0.000044
factor_w = 60.485234     factor_b = 17.613053
---------------------------------------------------------------------------------------------
w = 2.661517     b = 3.903263    z = 150.000000
delta_w = 0.000000   delta_b = 0.000000  delta_z = 0.000000
factor_w = 60.485224     factor_b = 17.613052
---------------------------------------------------------------------------------------------
result: 经过了4次迭代，最终b = 3.903263  w = 2.661517  此时精度为1e-5

每次迭代不更新factor_b和factor_w的结果

w = 2.666667     b = 3.904762    z = 162.000000
delta_w = 0.333333   delta_b = 0.095238  delta_z = 12.000000
factor_w = 63.000000     factor_b = 18.000000
---------------------------------------------------------------------------------------------
w = 2.661628     b = 3.903322    z = 150.181406
delta_w = 0.005039   delta_b = 0.001440  delta_z = 0.181406
factor_w = 63.000000     factor_b = 18.000000
---------------------------------------------------------------------------------------------
w = 2.661474     b = 3.903278    z = 150.005526
delta_w = 0.000154   delta_b = 0.000044  delta_z = 0.005526
factor_w = 63.000000     factor_b = 18.000000
---------------------------------------------------------------------------------------------
w = 2.661469     b = 3.903277    z = 150.000170
delta_w = 0.000005   delta_b = 0.000001  delta_z = 0.000170
factor_w = 63.000000     factor_b = 18.000000
---------------------------------------------------------------------------------------------
w = 2.661469     b = 3.903277    z = 150.000005
delta_w = 0.000000   delta_b = 0.000000  delta_z = 0.000005
factor_w = 63.000000     factor_b = 18.000000
---------------------------------------------------------------------------------------------
result: 经过了5次迭代，最终b = 3.903277  w = 2.661469  此时精度为1e-5

结果分析

• 每次更新factor_b和factor_w可有效减少所需的迭代次数，效率更高。
• 满足梯度下降的概念
• 最终得到结果是相同的