Approximation error: Difference between revisions

Revision as of 05:09, 14 November 2006

Revision as of 17:22, 21 November 2006

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where the vertical bars denote the [[absolute value]], ''a'' represents the true value, and ''b'' represents the approximation to ''a''.

==Propagation of Errors==

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>''' respectivly, we can use:

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

:<math>\epsilon z = \epsilon x + \epsilon y\,</math>

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

:<math>\epsilon z = |\epsilon x - \epsilon y|\,</math>

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

:<math>\eta z = \eta x + \eta y\,</math>

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

:<math>\eta z = |\eta x - \eta y|\,</math>

[[Category:Numerical analysis]]