Approximation error: Difference between revisions

Revision as of 17:47, 22 November 2021

Revision as of 17:50, 22 November 2021

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[[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 somea 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).

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

An approximation error can occur because of computing [[machine precision]] or [[measurement 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).