daviddoji/CalculusWithJuliaNotes.jl
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jverzani
2024-10-15 17:45:52 -04:00
parent 30086f9517
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quarto/derivatives/condition.qmd
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@@ -15,7 +15,7 @@ The *forward error* is $||f(x+\delta_x) - f(x)||$, the *relative forward error*
The *backward error* is $||\delta_x||$, the *relative backward error* is $||\delta_x|| / ||x||$.
The *absolute condition number* $\hat{\kappa}$ is worst case of this ratio $||\delta_f||/ ||\delta_x||$ as the pertubation size shrinks to $0$.
The *absolute condition number* $\hat{\kappa}$ is worst case of this ratio $||\delta_f||/ ||\delta_x||$ as the perturbation size shrinks to $0$.
The relative condition number $\kappa$ divides $||\delta_f||$ by $||f(x)||$ and $||\delta_x||$ by $||x||$ before taking the ratio.