Approximation error: Difference between revisions

Revision as of 17:50, 22 November 2021

Revision as of 17:53, 22 November 2021

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The '''approximation error''' in a data value is the discrepancy between an exact value and some ''[[approximation]]'' to it. This error can be expressed as an '''absolute error''' (the numerical amount of the discrepancy) or as a '''relative error''' (the absolute error divided by the data value).

An approximation error can occur because of computing [[machine precision]] or [[measurement error]] (e.g., the accurate readinglength of a piece of paper is 4.553 cm but since the ruler doesonly notallows useyou decimalsto estimate it to the nearest 0.1 cm, so you roundmeasure it toas 4.5  cm).

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