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[Solved] Just a little math question


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#1 CryZe   Members   -  Reputation: 768

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Posted 05 September 2012 - 12:19 PM

I have a function:
Posted Image

and I need two functions g(x) and h(y) where the following is true:
Posted Image

I don't know if it's possible, but it would greatly improve the quality of my algorithm.

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#2 Álvaro   Crossbones+   -  Reputation: 13935

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Posted 05 September 2012 - 12:27 PM

No, it cannot be done. The square root messes things up.

Consider this:
f(0,0) = 1
f(1,0) = e^-1
f(0,1) = e^-1

If g(x) and h(y) existed, you would have
g(0)*h(0) = 1
g(1)*h(0) = e^-1
g(0)*h(1) = e^-1
g(1)*h(1) = (g(1)*h(0)) * (g(0)*h(1)) / (g(0)*h(0)) = e^-2

But f(1,1) = e^-sqrt(2) instead.




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