Content deleted Content added
m rm unhelpful links |
Linear Algebra equvilance |
||
Line 1:
In the [[mathematics|mathematical]]
#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).
Line 17:
:<math>\eta = \frac{|a - b|}{|a|} </math>
if <math>|a|\ne 0</math> and the '''percent error''' is
:<math>\delta = \frac{|a-b|}{|a|}\times{}100\%</math>
where the vertical bars denote the [[absolute value]], ''a'' represents the true value, and ''b'' represents the approximation to ''a''.
==Linear Algebra Definition==
Where <math>\left\| a\right\|_p</math> is the [[Norm_%28mathematics%29#p-norm|p-norm]] of vertex ''a'', and <math>\hat{x}</math> is an approximation of vertex ''x'' where <math>x\in\mathbb{R}^n</math>.
*<math>\epsilon=\left\|\hat{x}-x\right\|_2</math>
*<math>\eta=\frac{\left\|\hat{x}-x\right\|_2}{\left\| x\right\|_2}</math>
*<math>\left\lceil -\operatorname{log}_{10}\left(\frac{\left\|\hat{x}-x\right\|_\infty}{\left\| x\right\|_\infty}\right)\right\rceil</math> is the number of [[Significant figures]] of the largest magnitude entry of x.<ref name="GOLUB_MAT_COMP2.2.3">{{cite book|last=Golub|first=Gene|authorlink=Gene_H._Golub|coauthors=Charles F. Van Loan|title=Matrix Computations - Third Edition|publisher=The Johns Hopkins University Press|date=1996|___location=Baltimore|pages=53|id=ISBN 0-8018-5413-X}}
</ref>
==Propagation of errors==
Line 45 ⟶ 53:
:<math>\eta z = |\eta x - \eta y|\,</math>
==References==
<!--<nowiki>
See http://en.wikipedia.org/wiki/Wikipedia:Footnotes for an explanation of how to generate footnotes using the <ref> and </ref> tags, and the template below.
</nowiki>-->
{{FootnotesSmall|resize=100%}}
[[Category:Numerical analysis]]
| |||