The Interval Analysis of Multilinear Expressions

Authors:
Cosimo Laneve;Tudor A. Lascu;Vania Sordoni
Affiliations:
Dipartimento di Scienze dell'Informazione, Universití di Bologna, Bologna, Italy;Dipartimento di Scienze dell'Informazione, Universití di Bologna, Bologna, Italy;Dipartimento di Matematica, Universití di Bologna, Bologna, Italy
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2010

Citing 4
Cited 0

Solving systems of polynomial inequalities in subexponential time

Journal of Symbolic Computation
A Generalized Interval Arithmetic

Proceedings of the International Symposium on Interval Mathemantics
The ASTREÉ analyzer

ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Symbolic methods to enhance the precision of numerical abstract domains

VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.