A sufficient condition for non-overestimation in interval arithmetic

The range of an arithmetic expression on an interval can be estimated by evaluating the expression using interval arithmetic. This gives always a superset of the range, which is usually proper. However, there are cases where no overestimation error occurs. The subject of this paper is to study such...

Full description

Saved in:
Bibliographic Details
Published inComputing Vol. 59; no. 4; pp. 349 - 363
Main Author Stahl, V.
Format Journal Article
LanguageEnglish
Published Wien Springer 01.01.1997
Subjects
Error analysis
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Polynomial
Sufficient condition
Error estimation
Expression evaluation
Minimal distance
Arithmetic expression
Arithmetic operation
Interval arithmetic
Online AccessGet full text

Cover

More Information
Summary:The range of an arithmetic expression on an interval can be estimated by evaluating the expression using interval arithmetic. This gives always a superset of the range, which is usually proper. However, there are cases where no overestimation error occurs. The subject of this paper is to study such cases systematically and to give a sufficient condition when interval evaluation yields the exact range. Testing the condition is inexpensive: Given the intermediate values which are obtained during the evaluation of the expression, only some comparisons and bookkeeping but no additional arithmetic operations need to be performed. We show that for certain classes of expressions there is no overestimation if the input interval has a sufficiently large distance to zero. Formulae for the minimal distance are derived for polynomials in Horner form and in factorized form.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0010-485X
1436-5057
DOI:10.1007/BF02684417