[Developers] [Patches] Make ADMConstraints GF public
Erik Schnetter
schnetter at cct.lsu.edu
Sun Sep 17 11:24:20 CDT 2006
On Sep 16, 2006, at 23:41:56, Jonathan Thornburg wrote:
> On Sat, 16 Sep 2006, Erik Schnetter wrote:
>> The "sum" reduction has the problem that it can easily lead to
>> large absolute
>> differences that are small relative differences. The "average"
>> reduction
>> behaves better in that respect, and, apart from that, tests the
>> same thing. I
>> suggest to avoid using the sum reduction in test cases.
>
> I'm confused: Since average := sum / sum_of_weights , why does
> average not also "lead to large absolute differences that are
> small
> relative differences"?
Because of the division by "sum_of_weights". If you assume 10^6 grid
points, then the absolute difference in the sum is 10^6 times the
absolution difference in the average. If you allow an absolute
difference of 10^-12, then there are often cases where the average is
deemed accurate enough, while the sum is deemed inaccurate.
Let me give an example:
Assume there are 10^6 grid points, all having the value 1.0 plus a
small error of the order of 10^-14. Then we have
the exact values:
average: 1.0
sum: 10^6
the perturbed values:
average: 1.0 + 10^-14
sum: 10^6 + 10^-8
The relative error of the perturbed values with respect to the
accurate values is 10^-14 for both the average and the sum. The
absolute errors differ; the absolute error for the average is 10^-14,
while the absolute error of the sum is 10^-8.
-erik
--
Erik Schnetter <schnetter at cct.lsu.edu>
My email is as private as my paper mail. I therefore support encrypting
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