Interval arithmetic

Method for bounding the errors of numerical computations Tolerance function (turquoise) and interval-valued approximation (red) Interval arithmetic (also known as interval mathematics, interval analysis or interval computation) is a mathematical technique used to mitigate rounding and measurement errors in mathematical computation by computing function bounds. Numerical methods involving interval arithmetic can guarantee relatively reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic or interval mathematics represents each value as a range of possibilities. Mathematically, instead of working with an uncertain real-valued variable x, interval arithmetic works with an interval [a, b] that defines the range of values that x can have. In other words, any value of the variable x lies in the closed interval between a and b. A function f, when applied to x, produces an interval [c, d] which includes all the possible values for f(x) for all x ∈ [a, b]. Interval arithmetic is suitable for a variety of purposes; the most common use is in scientific works, particularly when the calculations are handled by software, where it is