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

页码：43 / 53

页数：11

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