for real numbers x and dx gives a centered interval that contains the real interval .
CenteredInterval[x+ y,dx+ dy]
gives a centered interval that contains the complex rectangle .
for an approximate number c gives a centered interval that contains all values within the error bounds of c.
- Centered intervals are also known as center-radius or mid-radius intervals.
- CenteredInterval is typically used to obtain verified bounds on errors accumulated through numeric computation. Given error bounds for all arguments of a function, centered interval computation provides a reliable bound for the error in the function value.
- CenteredInterval[…] gives a centered interval object Δ with the center and the radius , where and are Gaussian rational numbers with power of two denominators. If and are real, then Δ represents the real interval , otherwise Δ represents the complex rectangle .
- Arithmetic operations and many mathematical functions work with centered interval arguments. f[Δ1,…,Δn] yields a centered interval object Δ which contains f[a1,…,an] for any ai∈Δi.
- IntervalMemberQ can be used to decide interval membership or inclusion between intervals.
- Relational operators such as Equal and Less yield explicit True or False results whenever they are given disjoint intervals.
- In StandardForm and related formats, CenteredInterval objects are printed in elided form, with only approximate values of the center and the radius displayed.
- Normal converts CenteredInterval objects to arbitrary-precision numbers with accuracy corresponding to the radius.
- Information[CenteredInterval[…], prop] gives the property prop of the center-radius interval. The following properties can be specified:
"Center" the center of the interval "Radius" the radius of the interval "Bounds" bounds on the values in the interval
Examplesopen allclose all
Basic Examples (3)
Constructing Center-Radius Intervals (7)
Convert a bounded Interval object to a centered interval:
Nonzero machine-precision numbers are treated as numbers with $MachinePrecision precise digits:
Interval Arithmetic (5)
Interval arithmetic operations return Indeterminate if the set of values is unbounded:
Interval Properties (5)
Use IntervalIntersection to compute the intersection:
The empty interval is expressed as Interval:
Properties & Relations (2)
Interval represents real intervals given by specifying their endpoints:
Convert the interval to CenteredInterval representation:
Wolfram Research (2021), CenteredInterval, Wolfram Language function, https://reference.wolfram.com/language/ref/CenteredInterval.html.
Wolfram Language. 2021. "CenteredInterval." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CenteredInterval.html.
Wolfram Language. (2021). CenteredInterval. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CenteredInterval.html