When is the product of intervals also an interval?

P.G. Vroegindeweij, O.M. Kosheleva

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)

    Abstract

    Interval arithmetic is based on the fact that for intervals on the real line, the element-wise product of two intervals is also an interval. This property is not always true: e.g., it is not true if we consider intervals on the set of integers instead of intervals on the set of real numbers. When is an element-wise product or a sum of two intervals always an interval? In this paper, we analyze this problem in a general algebraic setting: we need the corresponding algebraic structures to have (related) addition, multiplication, and order; thus, we consider (consistently) ordered rings. We describe all consistently ordered rings for which the element-wise product and sum of two intervals are always intervals.
    Original languageEnglish
    Pages (from-to)179-190
    Number of pages12
    JournalReliable Computing
    Volume4
    Issue number2
    DOIs
    Publication statusPublished - 1998

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