Approximation error: Difference between revisions

Revision as of 21:57, 9 September 2005

Revision as of 20:57, 4 October 2005

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In the [[mathematics|mathematical]] subfield of [[numerical analysis]] the '''approximation error''' in some data is the differencediscrepancy between thean exact value and thesome valueapproximation to usedit. An approximation error can occur because

#the measurement of the data is not precise (due to the instruments)

#we use an approximation instead of the real data (e.g. 3.14 instead of π)

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==Definition==

Given some value ''a'' and an approximation ''b'' of ''a'', the '''absolute error''' is

:<math>\epsilon := |a - b|</math>

and the '''relative error''' is

:<math>\eta := \frac{|a - b|}{|a|}. </math>

where the vertical bars denote the [[absolute value]].

[[Category:Numerical analysis]]