interval arithmetic - Definition. Was ist interval arithmetic
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Was (wer) ist interval arithmetic - definition

METHOD FOR BOUNDING THE ERRORS OF NUMERICAL COMPUTATIONS
Interval analysis; Interval methods; Interval-valued computation; Interval-valued computing; Extensions for Scientific Computation; XSC (floating point); Interval arithmetics; IEEE 1788-2015; IEEE 1788; IEEE P1788; IEEE P1788D9.3; Extension for Scientific Computation; Extension for Scientific Computing; Extensions for Scientific Computing; ACRITH; IBM ACRITH; C-XSC; FORTRAN-SC; Fortran-SC; ACRITH-XSC; Interval computation; Interval mathematics; Triplex number
  • Approximation of the [[normal distribution]] by a sequence of intervals
  • Rough estimate (turquoise) and improved estimates through "mincing" (red)
  • Outer bounds at different level of rounding
  • Approximate estimate of the value range
  • Treating each occurrence of a variable independently
  • Wrapping effect
  • Body mass index for different weights in relation to height L (in meters)
  • [[Body mass index]] for a person 1.80 m tall in relation to body weight ''m'' (in kilograms)
  • Reduction of the search area in the interval Newton step in "thick" functions.
  • Multiplication of positive intervals
  • Mean value form
  • Values of a monotonic function

simple interval         
  • b}}-major]] scale[[File:Ab major scale.mid]]
  • Ascending and descending chromatic scale on C[[File:ChromaticScaleUpDown.ogg]]
  • Enharmonic tritones: A4 = d5 on C[[File:Tritone on C.mid]]
  • Main intervals from C[[File:Intervals.mid]]
  • natural}}).[[File:Pythagorean comma on C.mid]]
  • Simple and compound major third[[File:Simple and compound major third.mid]]
  • Division of the measure/chromatic scale, followed by pitch/time-point series[[File:Time-point series.mid]]
PHYSICAL QUANTITY; RATIO BETWEEN TWO SONIC FREQUENCIES, OFTEN MEASURED IN CENTS, A UNIT DERIVED FROM THE LOGARITHM OF THE FREQUENCY RATIO
Musical interval; Simple and compound intervals; Compound interval; Perfect interval; Interval strength; Melodic interval; Vertical (music); Simple interval; Musical intervals; Harmonic Interval; Harmonic interval; Interval Pairs; Intervals (music); Music intervals; Interval root; Compound intervals; Perfect intervals; Minor interval; Major interval; Imperfect interval; Twelfth (music); Interval number; Interval quality; Sixth interval; Root (interval); Ratio (music); Musical ratio; Interval name; Interval (musical); Music interval
¦ noun Music an interval of one octave or less.
compound interval         
  • b}}-major]] scale[[File:Ab major scale.mid]]
  • Ascending and descending chromatic scale on C[[File:ChromaticScaleUpDown.ogg]]
  • Enharmonic tritones: A4 = d5 on C[[File:Tritone on C.mid]]
  • Main intervals from C[[File:Intervals.mid]]
  • natural}}).[[File:Pythagorean comma on C.mid]]
  • Simple and compound major third[[File:Simple and compound major third.mid]]
  • Division of the measure/chromatic scale, followed by pitch/time-point series[[File:Time-point series.mid]]
PHYSICAL QUANTITY; RATIO BETWEEN TWO SONIC FREQUENCIES, OFTEN MEASURED IN CENTS, A UNIT DERIVED FROM THE LOGARITHM OF THE FREQUENCY RATIO
Musical interval; Simple and compound intervals; Compound interval; Perfect interval; Interval strength; Melodic interval; Vertical (music); Simple interval; Musical intervals; Harmonic Interval; Harmonic interval; Interval Pairs; Intervals (music); Music intervals; Interval root; Compound intervals; Perfect intervals; Minor interval; Major interval; Imperfect interval; Twelfth (music); Interval number; Interval quality; Sixth interval; Root (interval); Ratio (music); Musical ratio; Interval name; Interval (musical); Music interval
¦ noun Music an interval greater than an octave.
Interval (mathematics)         
  • The addition ''x'' + ''a'' on the number line. All numbers greater than ''x'' and less than ''x'' + ''a'' fall within that open interval.
IN MATH, A SET OF REAL NUMBERS IN WHICH ANY NUMBER THAT LIES BETWEEN TWO NUMBERS IN THE SET IS ALSO INCLUDED IN THE SET
Interval on the real line; Closed interval; Open interval; Interval (analysis); Half-open interval; Half-closed interval; Interval notation; Interval of the real line; Bounded interval; Semi-open interval; Dyadic interval; Interval Notation; Range notation; Degenerate interval; Values interval; Subinterval; Open Interval; Proper subinterval; Endpoints (interval); Nondegenerate interval; Non-degenerate interval
In mathematics, a (real) 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 satisfying is an interval which contains , , and all numbers in between.

Wikipedia

Interval arithmetic

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 reliable and mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a range of possibilities.

Mathematically, instead of working with an uncertain real-valued variable x {\displaystyle x} , interval arithmetic works with an interval [ a , b ] {\displaystyle [a,b]} that defines the range of values that x {\displaystyle x} can have. In other words, any value of the variable x {\displaystyle x} lies in the closed interval between a {\displaystyle a} and b {\displaystyle b} . A function f {\displaystyle f} , when applied to x {\displaystyle x} , produces an interval [ c , d ] {\displaystyle [c,d]} which includes all the possible values for f ( x ) {\displaystyle f(x)} for all x [ a , b ] {\displaystyle x\in [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 used to keep track of rounding errors in calculations and of uncertainties in the knowledge of the exact values of physical and technical parameters. The latter often arise from measurement errors and tolerances for components or due to limits on computational accuracy. Interval arithmetic also helps find guaranteed solutions to equations (such as differential equations) and optimization problems.