Definition:Finite Difference Operator/Backward Difference
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Definition
Let $f: \R \to \R$ be a real function.
Let $h \in \R_{>0}$.
The backward difference operator on $f$ is defined as:
- $\map {\nabla_h f} x := \map f x - \map f {x - h}$
Unit Step Size
The backward difference operator can often be seen with a step size $h$ equal to $1$, as follows:
The backward difference operator on $f$ is defined as:
- $\map {\nabla f} x := \map f x - \map f {x - 1}$
Also see
- Results about the backward difference operator can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): backward difference
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): finite differences
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): finite differences
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): backward difference
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): backward difference