Order of approximation: Difference between revisions

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{{Short description|Expressions for approximation accuracy}}

{{original research|date=November 2024}}

{{Order-of-approx}}

{{unclear|date=March 2016}}

In [[science]], [[engineering]], and other quantitative disciplines, '''order of approximation''' refers to formal or informal expressions for how accurate an [[approximation]] is.

==Usage in science and engineering==

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: <math>y \sim x + 2.67.</math>

One should be careful though, because the multiplicative function will be defined for the whole interval. If only three data points are available, one has no knowledge about the rest of the [[Interval (mathematics)|interval]], which may be a large part of it. This means that ''y'' could have another component which equals 0 at the ends and in the middle of the interval. A number of functions having this property are known, for example ''y'' = sin π''x''. [[Taylor series]] isare useful and helpshelp predict an [[Closed-form expression|analytic solutionsolutions]], but the approximationapproximations alone doesdo not provide conclusive evidence.

===First-order===

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is an approximate fit to the data.

In this example there is a zeroth-order approximation that is the same as the first-order, but the method of getting there is different; i.e. a wild stab in the dark at a relationship happened to be as good as an "educated guess".

===Second-order===

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* [[Chapman–Enskog_theory#Mathematical_Formulation | Chapman–Enskog method]]

* [[Big O notation]]

* [[Order of accuracy]]

==References==