Approximation error: Difference between revisions

Revision as of 17:22, 21 November 2006

Revision as of 22:10, 3 December 2006

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In the [[mathematics|mathematical]] subfield of [[numerical analysis]] the '''approximation error''' in some data is the [[discrepancy]] between an exact value and some approximation to it. An approximation error can occur because

#the [[measurement]] of the [[data]] is not precise (due to the instruments), or

#approximations are used instead of the real data (e.g., 3.14 instead of π).

One commonly distinguishes between the '''relative error''' and the '''absolute error'''.

The [[numerical stability]] of an [[algorithm]] in numerical analysis indicates how the error is propagated by the algorithm.

==Definitions==

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When calculating using approximate values it is important to be able to calculate the errors involved.

For measured values '''X & Y''' with absolute errors '''<math>\epsilon x\,</math> & <math>\epsilon y\,</math>''' and relative errors '''<math>\eta x\,</math> & <math>\eta y\,</math>''' respectivlyrespectively, we can use:

* For <math>Z = X + Y\,</math>: