File:AbsoluteErrorNumericalDifferentiationExample.png

Summary[edit]

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Details[edit]

I made this using the graphics programming language TikZ, Beamer and LaTeX

The plot displays the absolute error when computing the derivative of ${\displaystyle f(x)=x^{3}}$ (${\displaystyle f'(x)=3x^{2}}$) using a forward difference (of first order) and a centered difference (of second order),

${\displaystyle {\frac {f(x+h)-f(x)}{h}}-3x^{2}}$

for various values of ${\displaystyle x}$. The centered difference is for ${\displaystyle x=0.1}$ only.

The noisy negative slope is due to finite precision (64-bit IEEE754) in the computer used, and the positive slope is due to the formula error of the differentiation formula.

Licensing[edit]

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.