interval arithmetic wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Interval_arithmeticInterval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using interval arithmetic can guarantee reliable, mathematically
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See moreThe main objective of interval arithmetic is a simple way to calculate upper and lower bounds for the range of a function in one or more variables. These endpoints are not necessarily the true supremum or infimum, since the precise
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The methods of classical numerical analysis can not be transferred one-to-one into interval-valued algorithms, as dependencies between numerical values are usually not taken into account.
Rounded interval arithmetic
To work effectively in a...
See moreA binary operation on two intervals, such as addition or multiplication, is defined by
In other words, it is the set of all possible values of , where and are in their corresponding intervals. If...
See moreAn interval can also be defined as a locus of points at a given distance from the centre, and this definition can be extended from real numbers to complex numbers. As it is the case with computing with real numbers, computing with complex numbers involves
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See moreInterval arithmetic can be used in various areas (such as set inversion, motion planning, set estimation or stability analysis) to treat estimates with no exact numerical value.
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See moreWikipedia text under CC-BY-SA license- https://simple.wikipedia.org/wiki/Interval_arithmetic
- For real intervals (interval of real numbers), interval arithmetic is defined as follows: 1. Addition: [ x 1 , x 2 ] + [ y 1 , y 2 ] = [ x 1 + y 1 , x 2 + y 2 ] {\displaystyle [x_{1},x_{2}]+[y_{1},y_{2}]=[x_{1}+y_{1},x_{2}+y_{2}]} 2. Subtraction: [ x 1 , x 2 ] − [ y 1 , y 2 ] = [ x 1 − y 2 , x 2 − y 1 ] {\displaystyle [x_{1},x_{2}]-[y_{1},y_{2}]=[x...
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- https://sco.wikipedia.org/wiki/Interval_arithmetic
Interval arithmetic is a computer arithmetic for (mathematical) intervals .
Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 3 mins
- https://en.wikipedia.org/wiki/Interval_(mathematics)
- In mathematics, a interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between. Other examples of intervals are the set of numbers such that 0 < x < 1, the set of all real numbers R {\di...
- https://simple.wikipedia.org/wiki/Interval_(mathematics)
In mathematics, an interval is a group of numbers that includes all numbers between the beginning and the end. Numbers that are larger than the beginning number and smaller than the end number are inside the interval, and numbers that are smaller than the beginning number or larger than the end number are not in the interval.
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- https://en.wikipedia.org/wiki/Talk:Interval_arithmetic
(Interval arithmetic is also one of the simplest ways to approximate the roots of an arbitrary polynomial.) There are also other interesting differentiable functions whose derivatives aren't even expressible in closed form, let alone solvable algebraically. Kragen Javier Sitaker ( talk) 00:45, 4 June 2014 (UTC) [ reply]
- https://en.wikipedia.org/wiki/Talk:Interval_(mathematics)
Intervals (1), (2), (3), (4), (10) and (11) are called bounded intervals and intervals (5), (6), (7), (8) and (9) unbounded intervals . Interval (10) is also known as a singleton . The length of the bounded intervals (1), (2), (3), (4) is b - a in each case. The total length of a sequence of intervals is the sum of the lengths of the intervals.
- https://en.wikipedia.org/wiki/Interval
Interval (mathematics), a range of numbers Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets A statistical level of measurement Interval estimate Interval (graph theory) Space-time interval, the distance between two points in 4-space Arts and entertainment Dramatic arts
- https://en.wikipedia.org/wiki/Affine_arithmetic
Affine arithmetic is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations of certain primitive variables, which stand for sources of uncertainty in the data or approximations made during the computation. Affine arithmetic is meant to be an improvement on interval arithmetic, and is similar to generalized interval …
- https://en.wikipedia.org/wiki/Floating-point_arithmetic
Interval arithmetic allows one to represent numbers as intervals and obtain guaranteed bounds on results. It is generally based on other arithmetics, in particular floating point. Computer algebra systems such as Mathematica, Maxima, and Maple can often handle irrational numbers like or
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