Question

define mean, absolute error, relative error​

Answer 1

Given some value v and its approximation vapprox, the absolute error is

{\displaystyle \epsilon =|v-v_{\text{approx}}|\ ,}\epsilon =|v-v_{\text{approx}}|\ ,

where the vertical bars denote the absolute value. If {\displaystyle v\neq 0,}v\neq 0, the relative error is

{\displaystyle \eta ={\frac {\epsilon }{|v|}}=\left|{\frac {v-v_{\text{approx}}}{v}}\right|=\left|1-{\frac {v_{\text{approx}}}{v}}\right|,}\eta ={\frac {\epsilon }{|v|}}=\left|{\frac {v-v_{\text{approx}}}{v}}\right|=\left|1-{\frac {v_{\text{approx}}}{v}}\right|,