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I have a function in discrete domain [tex]f:\mathbb{Z}\rightarrow \mathbb{R}[/tex], and I assume thatfis an approximation of another differentiable function [tex]g:\mathbb{R}\rightarrow \mathbb{R}[/tex].

In other words [tex]f(n)=g(n)[/tex], [tex]n\in \mathbb{Z}[/tex].

When one wants to approximate the first derivative ofg, it is possible to use theforward differenceorbackward differenceoperators, which are respecively:

[tex]\Delta f(n)=f(n+1)-f(n)[/tex]

[tex]\nabla f(n)=f(n)-f(n-1)[/tex]

My question is: is it common or allowed to use a mixture of these two operators in the following way:

[tex]g'(x) \approx \Delta f(x)[/tex] for [tex]x\geq 0[/tex]

[tex]g'(x) \approx \nabla f(x)[/tex] for [tex]x<0[/tex]

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# Discrete derivatives with finite-differences

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