网站首页  英汉词典

请输入您要查询的英文单词:

 

单词 Abel inequality
释义

Abel inequality

中文百科

阿贝尔不等式 Abel's inequality

(重定向自Abel inequality)

阿贝尔不等式Abel's inequality),由尼尔斯·阿贝尔提出,给出了两个矢量内积绝对值的上界。

设{a1, a2,...}为单调递减或单调递增的实数集并设{b1, b2,...}为实数集或复数集。

如果{an}单调递增:


\left |\sum_{k=1}^n a_k b_k \right | \le \operatorname{max}_{k=1,\dots,n} |B_k| (|a_n| + a_n - a_1),

B_k =b_1+\cdots+b_k.

如果{an}单调递减:


\left |\sum_{k=1}^n a_k b_k \right | \le \operatorname{max}_{k=1,\dots,n} |B_k| (|a_n| - a_n + a_1),

阿贝尔不等式可从阿贝尔变换轻易得出:


\sum_{k=1}^n a_k b_k = a_n B_n - \sum_{k=1}^{n-1} B_k (a_{k+1} - a_k).
英语百科

Abel's inequality 阿贝尔不等式

(重定向自Abel inequality)

In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.

Let {a1, a2,...} be a sequence of real numbers that is either nonincreasing or nondecreasing, and let {b1, b2,...} be a sequence of real or complex numbers. If {an} is nondecreasing, it holds that

随便看

 

英汉网英语在线翻译词典收录了3779314条英语词汇在线翻译词条,基本涵盖了全部常用英语词汇的中英文双语翻译及用法,是英语学习的有利工具。

 

Copyright © 2004-2024 encnc.com All Rights Reserved
更新时间:2025/6/22 20:16:10