Approximation error: Difference between revisions

Revision as of 05:01, 16 June 2021

Revision as of 17:44, 22 November 2021

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{{broader|Approximation}}

[[File:E^x with linear approximation.png|thumb|Graph of <math>f(x) = e^x</math> (blue) with its linear approximation <math>P_1(x) = 1 + x</math> (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0.]]

The '''approximation error''' in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because:

#the [[measurement]] of the [[data]] is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5&nbsp;cm but since the ruler does not use decimals, you round it to 5&nbsp;cm.) or

#approximations

The '''approximation error''' in some data is the discrepancy between an exact value and some ''[[approximation]]'' to it. An approximation error can occur because:

It can be distinguished between '''relative error''' and '''absolute error'''.

#theAn [[measurement]]approximation error can occur because of thecomputing [[datamachine precision]] isor not[[measurement precise due to the instruments.error]] (e.g., the accurate reading of a piece of paper is 4.5&nbsp;cm but since the ruler does not use decimals, you round it to 5&nbsp;cm).) or

In the [[mathematics|mathematical]] field of [[numerical analysis]], the [[numerical stability]] of an [[algorithm]] indicates how the error is propagated by the algorithm.

==Formal Definitioncefinition==

One commonly distinguishes between the relative error and the absolute error.