Sharpness in interval computations
type: Item
instance of: scholarly article
title: Sharpness in interval computations
zbMATH Open document ID: 0881.65032
DOI: 10.1023/A:1009917818868
author: Eldon R. Hansen
published in: Reliable Computing
publication date: 1998-02-16T00:00:00Z
review text: If \(f(x)\) is an arithmetic expression for the multivariate rational function \(f\), the interval extension \(f(X)\) arises from \(f(x)\) by replacing the variable \(x\) by the interval or interval variable \(X\). In general, \(f(X)\) is a proper superset of the range of \(f\) over \(X\). -- The author pursues an interesting concept to determine whether \(f(X)\) is equal to the range or whether one of the endpoints of \(f(X)\) coincides with an endpoint of the range. This concept is based on a so-called endpoint arithmetic, where the dependency of the endpoints of \(f(X)\) on the endpoints of \(X\) is investigated.
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 1045479
zbMATH Keywords: interval arithmetic
zbMATH Keywords: multivariate rational function
zbMATH Keywords: interval extension
zbMATH Keywords: range
zbMATH Keywords: endpoint arithmetic
reviewed by: H. Ratschek
MaRDI profile type: Publication
full work available at URL: a:1009917818868
OpenAlex ID: W162001771
description: scientific article; zbMATH DE number 1045479