Approximation error: Difference between revisions

Revision as of 13:29, 28 January 2024

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An approximation error can occur for a variety of reasons, among them a computing [[machine precision]] or [[measurement error]] (e.g. the length of a piece of paper is 4.53 cm but the ruler only allows you to estimate it to the nearest 0.1 cm, so you measure it as 4.5 cm).

In the [[mathematics|mathematical]] field of [[numerical analysis]], the [[numerical stability]] of an [[algorithm]] indicates the extent to which errors in the input of the algorithm will lead to large errors of the output; numerically stable algorithms todo not yield a significant error in output when the input is malformed and vice versa.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Numerical Stability |url=https://mathworld.wolfram.com/ |access-date=2023-06-11 |website=mathworld.wolfram.com |language=en}}</ref>

==Formal definition==