Anonymous user
Talk:Numeric error propagation: Difference between revisions
Different propagation for mul and exp?
(Different propagation for mul and exp?) |
|||
Line 38:
: Multiplication by a negative constant didn't seem right either so I fixed that. Thanks. --[[User:Paddy3118|Paddy3118]] 12:44, 17 August 2011 (UTC)
:: It's not pertinent to current task, but a negative uncertainty does have meaning if correlation is considered. If <math>a\equiv a_0\pm\sigma</math>, you can say <math>-a=-a_0\pm(-\sigma)</math>, and the sum <math>a + (-a) = 0\pm 0</math> (note how the <math>\sigma</math>s just add, not RMS). --[[User:Ledrug|Ledrug]] 12:58, 17 August 2011 (UTC)
==Do multiplication and exponentiation propagate differently?==
Do I misunderstand the formulae, or do multiplication and exponentiation indeed result in different error propagations?
If I look at the square of the uncertainties for a*a vs. a^2:
f = a*a
σ[f]^2 =
f^2 * ((σ[a] / a)^2 + (σ[a] / a)^2) =
(a*a)^2 * 2 * (σ[a] / a)^2 =
a*a*a*a * 2 * σ[a]^2 / a^2
f = a^2
σ[f]^2 =
(f * c * σ[a] / a)^2 =
f^2 * c^2 * σ[a]^2 / a^2 =
a*a*a*a * 2 * 2 * σ[a]^2 / a^2
Take a = 100 ± 2. For a*a I get an error of 282.84, while for a^2 I get 400.00. --[[User:Abu|Abu]] 10:01, 18 August 2011 (UTC)
| |||