Hend Dawood
2019-04-01
<p>Interval arithmetic is a fundamental and reliable mathematical machinery for scientific computing and for addressing uncertainty in general. In order to apply interval mathematics to real life uncertainty problems, one needs a computerized (machine) version thereof, and so, this article is devoted to some mathematical notions concerning the algebraic system of machine interval arithmetic. After formalizing some purely mathematical ingredients of particular importance for the purpose at hand, we give formal characterizations of the algebras of real intervals and machine intervals along with describing the need for interval computations to cope with uncertainty problems. Thereupon, we prove some algebraic and order-theoretic results concerning the structure of machine intervals.</p>
https://doi.org/10.5281/zenodo.2656089
oai:zenodo.org:2656089
eng
Zenodo
https://doi.org/10.5281/zenodo.2702404
https://zenodo.org/communities/mathscicu
https://zenodo.org/communities/omj
https://doi.org/10.5281/zenodo.2656088
info:eu-repo/semantics/openAccess
Creative Commons Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/legalcode
Online Mathematics Journal, 01(02), 1–13, (2019-04-01)
Interval mathematics
Machine interval arithmetic
Outward rounding
Floating-point arithmetic
Machine monotonicity
Dense orders
Orderability of intervals
Orderability of intervals
Singletonicity
Subdistributive semiring
S-semiring
On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic
info:eu-repo/semantics/article