| 二重幂平均不等式的优化与机器实现 |
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| 引用本文： | 文家金,罗钊.二重幂平均不等式的优化与机器实现[J].成都大学学报(自然科学版),2008,27(3). |
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| 作者姓名： | 文家金 罗钊 |
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| 作者单位： | 成都大学,信息科学与技术学院,四川,成都,610106;成都大学,信息科学与技术学院,四川,成都,610106 |
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| 基金项目： | 国家自然科学基金资助项目，四川省教育厅自然科学重点项目资助 |
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| 摘 要： | 定义了正实数组a的t次二重幂平均Mt]m,n(a;α;λ),获得了使不等式Mr]m,n(a;α;λ)≤(≥)Mnθ](a)成立的机器可实现的充要条件和充分条件,借助于Mathematica数学软件给出了一些算例.这里,Mnθ](a)为正实数组a的θ次幂平均,m,n≥2,min{α}<θ0,采用的方法是降维法.
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| 关 键 词： | 幂平均 二重幂平均 降维法 |
Optimization and Computer Actualization of Inequalities Involving the Double Power Means |
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| WEN Jiajin,LUO Zhao.Optimization and Computer Actualization of Inequalities Involving the Double Power Means[J].Journal of Chengdu University (Natural Science),2008,27(3). |
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| Authors: | WEN Jiajin LUO Zhao |
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| Institution: | WEN Jiajin,LUO Zhao(College of Information Science , Technology,Chengdu University,Chengdu 610106,China) |
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| Abstract: | For a set of positive quantities,the double power mean Mr]m,n(a;α;λ) of order t is definited.We obtain a sufficient and necessary condition such that Mr]m,n(a;α;λ)≤(≥)Mθ]n(a) holds,and can be dealed with computer.Using Mathematica we give several numerical examples.Here Mθ]n(a) is the power mean of the set a and order θ,and m,n≥2,min{α}<θ0.Methods used here are procedures of descending dimension. |
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| Keywords: | power mean double power mean procedure of descending dimension |
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