Definition:Error/Absolute
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Definition
Let $x_0$ be an approximation to a (true) value $x$.
The absolute error of $x_0$ in $x$ is defined as:
- $\Delta x := x_0 - x$
Correction
The correction to $x$ is the quantity that needs to be added to $x_0$ to change it to $x$.
That is, the correction to $x$ is defined as $-\Delta x$.
Also defined as
The absolute error of $x_0$ in $x$ can also be seen defined as:
\(\text {(1)}: \quad\) | \(\ds \Delta x\) | \(:=\) | \(\ds x - x_0\) | |||||||||||
\(\text {(2)}: \quad\) | \(\ds \Delta x\) | \(:=\) | \(\ds \size {x_0 - x}\) |
where $\size {x_0 - x}$ denotes the absolute value of $x_0 - x$.
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: $3.5.1$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): error: 1.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): absolute error
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): error
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): absolute error
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): error