An optimization problem concerning multiplicative functions
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- 作者：Titus Hilberdink t.w.hilberdink@reading.ac.uk" class="auth_mail" title="E-mail the corresponding author
- 关键词：11A05 ; 11C20 ; 11N99 ; 15A36
- 刊名：Linear Algebra and its Applications
- 出版年：2015
- 出版时间：15 November 2015
- 年：2015
- 卷：485
- 期：Complete
- 页码：289-304
- 全文大小：341 K
文摘
In this paper we study the problem of maximizing a quadratic form 銆圓x,x銆?/span> subject to 鈥杧鈥?sub>q=1, where A has matrix entries 
with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that a369bbbeeba0c7fab5" title="Click to view the MathML source">0<f(p)<1, the solution is at a multiplicative point for all q≥1.
with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that a369bbbeeba0c7fab5" title="Click to view the MathML source">0<f(p)<1, the solution is at a multiplicative point for all q≥1.© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |