Image:AbsoluteErrorNumericalDifferentiationExample.png

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Image:AbsoluteErrorNumericalDifferentiationExample.png

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[edit] Summary

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

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

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

for various values of $x$ . The centered difference is for $x = 0.1$ 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.

[edit] Licensing

I, the creator of this work, hereby release it into the public domain. This applies worldwide.
In case this is not legally possible,
I grant any entity the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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(del) (cur) 17:44, 19 January 2007 . . Berland (Talk | contribs) . . 1548×914 (167,534 bytes) (I made this using the graphics programming language TikZ, Beamer and LaTeX The plot displays the ''absolute'' error when computing the derivative of <math>f(x)=x^3</math> using a forward difference)