從Nesterov的工作開始，最近關於隨機座標下降演算法的理論和應用已經進行了大量工作，表明隨機座標選擇準則能達到與高斯-索思韋爾選擇準則相同的收斂速度。

There has been significant recent work on the theory and application ofrandomized coordinate descent algorithms, beginning with the work of Nesterov,who showed that a random-coordinate selection rule achieves the sameconvergence rate as the Gauss-Southwell selection rule.

研究結果表明，我們永遠不應該使用高斯-索思韋爾準則，因為它通常比隨機選擇複雜得多。

This result suggests that we should never use the Gauss-Southwell rule,because it is typically much more expensive than random selection.

然而，這些演算法的經驗行為與此理論結果相抵觸：在選擇準則的計算成本可比擬的應用中，高斯-索思韋爾選擇準則傾向於具有比隨機座標選擇更好的效能。

However, the empirical behaviours of these algorithms contradict thistheoretical result: in applications where the computational costs of theselection rules are comparable, the Gauss-Southwell selection rule tends toperform substantially better than random coordinate selection.

我們對高斯-索思韋爾準則進行了簡單的分析，結果表明，除了極端情況，它的收斂速度比隨機座標選擇要更快一些。

We give a simple analysis of the Gauss-Southwell rule showingthat—except in extreme cases—its convergence rate is faster than choosingrandom coordinates.

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