Definition:Error/Relative
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Definition
Let $x_0$ be an approximation to a (true) value $x$.
The relative error of $x_0$ in $x$ is defined as:
- $\delta x := \dfrac {\Delta x} x$
where $\Delta x$ denotes the absolute error of $x_0$.
This can be defined only when $x \ne 0$.
Also defined as
The relative error of $x_0$ in $x$ can also be defined as:
- $\delta x \approx \dfrac {\Delta x} {x_0}$
where:
- $\Delta x$ denotes the absolute error of $x_0$
- $\approx$ indicates that the value is but approximate.
This can be particularly useful when the true value $x$ can only be speculated.
Also see
- Results about errors can be found here.
Sources
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.5$ Absolute and Relative Errors: $3.5.2$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): error: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relative error
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relative error
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): relative error