Definition:Calculation Rounding Error
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Definition
Let $S$ be a set of continuous data.
Let $\map C S$ be a calculation which is to be made on $S$.
The calculation rounding error of $S$ is defined as:
- $R = \size {\map C S - \overline {\map C {\overline S} } }$
where:
- $\overline x$ denotes the rounded value of a given $x$
- $\size {\, \cdot \,}$ denotes the absolute value function.
Examples
Arbitrary Example
Consider the equation:
- $x = \dfrac 1 {1 - \cos 1 \degrees}$
Evaluating the calculation while rounding to $4$ decimal places gives:
- $x = 5000$
but the true value is $6565.8$ to $1$ decimal place.
Hence the calculation rounding error of this calculation is $1.6565.8$, or some $24 \%$ or $31 \%$ relative error, depending on how the latter is calculated.
Also see
- Definition:Cumulative Rounding Error, an instance of a calculation rounding error
- Results about calculation rounding errors can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): error: 1. (in numerical computation) Rounding (or roundoff) errors
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): error: 1. (in numerical computation) Rounding (or roundoff) errors