Definition:Finite Difference Operator/Backward Difference

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

• Definition:Forward Difference Operator
• Definition:Central Difference Operator

• 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