Diff for "GeometricMean"

Differences between revisions 3 and 5 (spanning 2 versions)

The geometric mean of P1,..,Pn is

<<latex($$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$)>>

where <<latex($$Normalized(P_i) = \frac{P_i}{Pn}$$)>> where n is the referenced execution time. Obviously the geometic mean of the referenced machine is 1.

One of the nice features of Geometric means is that the following property holds:

<<latex($$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$)>>

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-  ⇤ ← Revision 3 as of 2004-02-18 00:05:51 → 
  Size: 646
  Editor: yakko
  Comment:
+   ← Revision 5 as of 2009-09-06 16:03:55 → ⇥
  Size: 518
  Editor: 24-183-238-75
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 5:
-{{{
                        _____________ 
                       / n 
Geometric Mean =    n / __ 
                     /  ||  Normalized(Pi) 
                   \/   i=1
+<<latex($$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$)>>
-Line 12:
+Line 7:
-     where Normalized(Pi) = Pi / Pn where n is the referenced execution time. Obviously the 
     geometic mean of the referenced machine is 1.
+where <<latex($$Normalized(P_i) = \frac{P_i}{Pn}$$)>> where n is the referenced execution time. Obviously the geometic mean of the referenced machine is 1.
-Line 15:
+Line 9:
-}}}
-Line 19:
+Line 13:
-{{{
                        GeometricMean(Xi)
GeometricMean(Xi/Yi) = ------------------
                        GeometricMean(Yi)
}}}
+<<latex($$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$)>>