Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to
put bounds on
rounding error
A roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are d ...
s and
measurement error
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a "mistake ...
s in
mathematical computation.
Numerical methods using interval
arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
can guarantee reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a
range of possibilities. For example, instead of saying the height of someone is approximately 2 meters, one could using interval arithmetic, say that the height of the person is definitely between 1.97 meters and 2.03 meters.
Mathematically, using interval arithmetic, instead of working with an uncertain
real-valued variable
, one works with an interval