Journal article Open Access

On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic

Hend Dawood

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.

Files (419.8 kB)
Name Size
On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic.pdf
md5:20819ea17591e72f13bbbfb8cdd840d4
419.8 kB Download
390
367
views
downloads
All versions This version
Views 390391
Downloads 367367
Data volume 154.1 MB154.1 MB
Unique views 288289
Unique downloads 264264

Share

Cite as