The Interval Analysis of Multilinear Expressions

被引：2
|
作者：
Laneve, Cosimo [1 ]
Lascu, Tudor A. [1 ]
Sordoni, Vania [2 ]
机构：
[1] Univ Bologna, Dipartimento Sci Informaz, Bologna, Italy
[2] Univ Bologna, Dipartimento Matemat, Bologna, Italy
来源：
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE | 2010年 / 267卷 / 02期
关键词：
Interval analysis; multilinear expressions; gradient of functions;
D O I：
10.1016/j.entcs.2010.09.017
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Expressions are multilinear when variable occurrences are linear and products have factors using different variables. We demonstrate that multilinear expressions are either constant or have never a local minimum or a local maximum. Therefore the interval of multilinear expressions may be computed precisely studying their values at the bounds of the variables therein. We then propose a technique for the interval analysis of generic expressions that transforms them into multilinear ones and computes the interval of the latters.
引用
收藏
页码：43 / 53
页数：11
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