Approximation Error
The short answer · 10 words
In short
Deviation that arises when a mathematical result is only approximated.
Flow-alerta.cab (2026): Approximation Error. https://flow-alerta.cab/en/glossar/approximation-error. Editorially reviewed on: 09 October 2026.
How much detail would you like?
Practical
Helps to weigh accuracy and computational effort in simplified calculations.
Example scenario: An area under a curve is approximated by trapezoid and compared with a more accurate reference.
For simulations and simplified calculations, specify the required accuracy and appropriate comparative values.
At a glance
- Core
- An approximation error describes the deviation between a target value or a target function and a selected approximation. The size depends on the method, presentation and error measure. It must be distinguished from additional rounding errors of the concrete calculation.
- Use
- Helps to weigh accuracy and computational effort in simplified calculations.
- Example
- Example scenario: An area under a curve is approximated by trapezoid and compared with a more accurate reference.
- Limits
- Express approximation as an exact value; do not name the error measure; mix approximation and rounding errors.
In context
Questions about this term
Does every mistake disappear with faster calculation?
No, the approximation procedure is crucial.
Is any approximation inappropriate?
No, the accuracy must fit the purpose.
All details and background
An approximation error describes the deviation between a target value or a target function and a selected approximation. The size depends on the method, presentation and error measure. It must be distinguished from additional rounding errors of the concrete calculation.
ELI5 – Explained simply
You replace a curved course with simple pieces and check how far they deviate from the original.
Why it matters in practice
Helps to weigh accuracy and computational effort in simplified calculations.
Example
Example scenario: An area under a curve is approximated by trapezoid and compared with a more accurate reference.
Pitfalls and limits
- Express approximation as an exact value; do not name the error measure; mix approximation and rounding errors.
Origin & history
Numerical mathematics examines approximations and errors systematically. MIT teaching material shows this through numerical integration.
Use in mid-sized companies
- For simulations and simplified calculations, specify the required accuracy and appropriate comparative values.
Related terms
- Numerical precision
- Algorithmic efficiency
Matching Flow-alerta service
AI opportunity analysis & roadmapAI consulting: AI potential analysis & roadmap on tasks, data and prerequisites of a possible first AI use case.Matching tool / use case
View use casesUse Case: Comparison of an approximation with a reliable reference.Sources
- ocw.mit.eduMIT, Numerical integration and the redemption of the trapezoidal rule
Quellenprüfung: 09.10.2026. Definition und dokumentierte Einordnung abgeglichen; Beispiele beschreiben mögliche Anwendungen.
Editorially reviewed on: