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Machine epsilon: Measurement, Standards & Science

Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject of computational science. The quantity is also called macheps and it has the symbols Greek epsilon ε…

Language: English [EN]
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Machine epsilon topic overview

The analysis highlights Measurement, Standards and Science as prominent areas in the source structure around Machine epsilon.

Related topics
42
Source areas
3
Connected nodes
45
Extracted relationships
37
Concept neighborhoods
19
Bridge connections
45

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Alternative definitions for epsilon · 22 topics
How to determine machine epsilon · 11 topics
Overview · 9 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Alternative definitions for epsilon

How to determine machine epsilon

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Machine epsilon connects Entity context

The extracted context around Machine epsilon shows recurring relationship patterns in the source. For example, Machine epsilon → Ada, By, Fortran, Mathematica, MATLAB, Numerical Recipes, Octave, Pascal, Press, Python, Rust, This Another extracted example is Machine epsilon → Computing, Double, EPSILON/java, EPSILONin Java, Float, Note, The, Where. Use these groups to spot repeated connection types before inspecting the individual relationships.

Machine epsilon

Top relations

related to Mainstream definition (Interval machine epsilon) · 12
Machine epsilon → Ada, By, Fortran, Mathematica, MATLAB, Numerical Recipes, Octave, Pascal, Press, Python, Rust, This
related to How to determine machine epsilon · 8
Machine epsilon → Computing, Double, EPSILON/java, EPSILONin Java, Float, Note, The, Where
related to Formal definition (Rounding machine epsilon) · 7
Machine epsilon → For, James Demmel, LAPACK, Most, Prof, Rounding, The
is a · 4
Machine epsilon → bound for relative error, difference between 1 and the next larger floating point number, maximum relative error of the chosen rounding procedure.Some background is needed to determine a value from this definition, one used by Prof
related to Alternative definitions for epsilon · 2
Machine epsilon → The, The IEEE
related to Approximation · 1
Machine epsilon → The
related to Values for standard hardware arithmetics · 1
Machine epsilon → The

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

epsilon machine displaystyle rounding definition number used error relative floating point also numbers varepsilon formal mainstream unit arithmetic value two

Machine epsilon relationships Subject–Predicate–Object triples

TTTA extracted 37 structured relationships around Machine epsilon. Examples in this analysis include Machine epsilon → is a → difference between 1 and the next larger floating point number and Machine epsilon → is a → one used by Prof. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Machine epsilonis adifference between 1 and the next larger floating point number0.90text
Machine epsilonis aone used by Prof0.90text
Machine epsilonis amaximum relative error of the chosen rounding procedure.Some background is needed to determine a value from this definition0.90text
Machine epsilonis abound for relative error0.90text
addition or multiplicationinstance ofis an arithmetic operation on floating-point numbers0.80text
andinstance ofis an arithmetic operation on floating-point numbers0.80text
Machine epsilonrelated to Alternative definitions for epsilonThe IEEE0.60section
Machine epsilonrelated to Alternative definitions for epsilonThe0.60section
Machine epsilonrelated to ApproximationThe0.60section
Machine epsilonrelated to Formal definition (Rounding machine epsilon)The0.60section
Machine epsilonrelated to Formal definition (Rounding machine epsilon)Prof0.60section
Machine epsilonrelated to Formal definition (Rounding machine epsilon)James Demmel0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Machine epsilon bring nearby vocabulary together. In this analysis, examples include Machine, Rounding and Error. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Machine epsilon
    • Machine
    • Rounding
    • Error
    • Number
    • Relative
    • Used
    • Unit
    • Definition
    • Displaystyle
    • Floating
    • Point
    • Following
  • machine epsilon
    • Machine
    • Rounding
    • Definition
    • Error
    • Number
    • Formal
    • Mainstream
    • Relative
    • Used
    • Unit
    • Displaystyle
    • Floating
  • relative approximation error
    • Relative
    • Rounding
    • Displaystyle
    • Numbers
    • Machine
    • Value
    • Varepsilon
    • Number
    • Also
    • Magnitude
    • Following
    • P-1
  • floating point
    • Point
    • Number
    • Precision
    • Larger
    • Next
    • System
    • Unit
    • Definition
    • Machine
    • Simply
    • Spacing
    • Mainstream
  • epsilon
    • Machine
    • Rounding
    • Definition
    • Error
    • Formal
    • Mainstream
    • Relative
    • Displaystyle
    • Used
    • Roundoff
    • Use
    • Number
  • interval machine epsilon or mainstream definition
    • Machine
    • Formal
    • Mainstream
    • Next
    • Simply
    • Rounding
    • Definition
    • Epsilon
    • Error
    • Larger
    • Number
    • Used
  • real number
    • Point
    • Textstyle
    • Larger
    • Next
    • Simply
    • Relative
    • Positive
    • System
    • Varepsilon
    • Rounding
    • Mach
    • Left
  • number system
    • Point
    • Textstyle
    • Larger
    • Next
    • Simply
    • Relative
    • Positive
    • System
    • Varepsilon
    • Rounding
    • Mach
    • Left

Connections between topic areas Semantic bridges

For Machine epsilon, one of the stronger structural bridges in this analysis connects Machine epsilon with Alternative definitions for epsilon. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Machine epsilon — Alternative definitions for epsilon · splits 23 ⟂ 23
Machine epsilon — How to determine machine epsilon · splits 34 ⟂ 12
Machine epsilon — Overview · splits 36 ⟂ 10

Map overview Semantic statistics

Machine epsilon

Nodes46
Edges45
Triples37
Avg. degree1.96
Density0.043478
Components1

Source & methodology

TTTA analyzes the structure around Machine epsilon to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Measurement, Standards & Science, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Machine epsilon · EN edition · Analysis: TopicsToTalkAbout

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