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切比雪夫總和不等式 - Wikipedia

切比雪夫總和不等式

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數學上的切比雪夫總和不等式，是以切比雪夫命名。它可以比較兩組數積的和及兩組數的線性和的積的大小：

若

a_1 \geq a_2 \ge \cdots \geq a_n

和

b_1 \geq b_2 \ge \cdots \geq b_n，

則有

n \sum_{k=1}^n a_kb_k \ge \left(\sum_{k=1}^n a_k\right)\left(\sum_{k=1}^n b_k\right) \ge n \sum_{k=1}^n a_kb_{n+1-k}。

上式也可以寫作

\frac1n \sum_{k=1}^n a_kb_k \ge \left(\frac1n \sum_{k=1}^n a_k\right)\left(\frac1n \sum_{k=1}^n b_k\right) \ge \frac1n \sum_{k=1}^n a_kb_{n+1-k}。

它是由排序不等式而來。

[编辑] 外部鏈結

Mathworld: Chebyshev Sum Inequality

来自“http://zh.wikipedia.org../../../%E5%88%87/%E6%AF%94/%E9%9B%AA/%E5%88%87%E6%AF%94%E9%9B%AA%E5%A4%AB%E7%B8%BD%E5%92%8C%E4%B8%8D%E7%AD%89%E5%BC%8F.html”
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