Approximation error
Error bounds, also called error limits, see the error calculation, measurement technology and the use of numerical analysis. An error bound is given by the Greek letter ( epsilon) and defines an agreed or guaranteed, approved extreme deviation from a target value. An error bound can be equated with a tolerance value.
- 2.1 Measurement Technology
- 2.2 Numerics
Definition
Be a true value ( setpoint) and an approximation of the exact value, so that:
If it is so called absolute error bound.
If true, this means relative error bound.
Remark
In keeping with the concept of error bound, but supported by standardization, the terms
- In metrology: " margin of error " and in a recent standard " deviation limit "
- In quality management and statistics: "Deviation limit amount ".
Application
Measurement
The margin of error is in the measurement technique of the utmost importance. It is not possible to carry out a one hundred percent accurate measurement. A measurement procedure is basically a measurement deviation ( previous terms: measurement error ) afflicted. The limiting error is the tolerable error of measurement for the given possibilities here.
Numerics
When calculating with floating-point numbers is inevitable to rounding error, since the number of places is limited ( size of the mantissa). Have two floating-point numbers can be compared with each other under an algorithm or calculation rule, the error sensor should be considered in the comparison. Especially with numerical methods that converge to a certain value, the use of an error bound is essential as a result of the limited number of points of a floating-point number, the value will never reach exactly usually the setpoint.