请输入您要查询的字词:

 

单词 PowerMean
释义

power mean


The r-th power meanMathworldPlanetmath of the numbers x1,x2,,xn is defined as:

Mr(x1,x2,,xn)=(x1r+x2r++xnrn)1/r.

The arithmetic meanMathworldPlanetmath is a special case when r=1.The power mean is a continuous functionMathworldPlanetmathPlanetmath of r, and taking limit when r0 gives us the geometric meanMathworldPlanetmath:

M0(x1,x2,,xn)=x1x2xnn.

Also, when r=-1 we get

M-1(x1,x2,,xn)=n1x1+1x2++1xn

the harmonic meanMathworldPlanetmath.

A generalizationPlanetmathPlanetmath of power means are weighted power means.

Titlepower mean
Canonical namePowerMean
Date of creation2013-03-22 11:47:17
Last modified on2013-03-22 11:47:17
Ownerdrini (3)
Last modified bydrini (3)
Numerical id14
Authordrini (3)
Entry typeDefinition
Classificationmsc 26D15
Classificationmsc 16D10
Classificationmsc 00-01
Classificationmsc 34-00
Classificationmsc 35-00
Related topicWeightedPowerMean
Related topicArithmeticGeometricMeansInequality
Related topicArithmeticMean
Related topicGeometricMean
Related topicHarmonicMean
Related topicGeneralMeansInequality
Related topicRootMeanSquare3
Related topicProofOfGeneralMeansInequality
Related topicDerivationOfZerothWeightedPowerMean
Related topicDerivationOfHarmonicMeanAsTheLimitOfThePowerMean
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 12:22:32