0

I understand that the absolute error of a function $f(x)$ where $f(x^*)$ is an approximation and $f$ is continuously differentiable can be written as

$$f(x)-f(x^*)\approx f'(x^*)(x-x^*)$$

To find the relative error we take:

$$\frac{f(x)-f(x^*)}{f(x)}\approx \frac{f'(x^*)(x-x^*)}{f(x)}\approx_{(1)} \frac{f'(x)}{f(x)}x\cdot\delta(x)$$

What steps got us to $\approx_{(1)} \frac{f'(x)}{f(x)}x\cdot\delta(x)$?

gbox
  • 12,867

1 Answers1

1

$δ(x)$ is the relative error in $x$, $$ δ(x)=\frac{x−x^∗}{x}. $$ One needs to insert the factor/divisor $x$ via $1=\frac xx$.

Lutz Lehmann
  • 126,666