Approximation error
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In the mathematical subfield of numerical analysis the approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because
- the measurement of the data is not precise (due to the instruments), or
- we use approximations instead of the real data (e.g., 3.14 instead of π).
The numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.
Definitions
Given some value a and an approximation b of a, the absolute error is
- [\epsilon = |a - b|\,]
- [\eta = \frac
>
>
] and the percent error is - [\delta = \frac
>
>
\times100\%] where the vertical bars denote the absolute value.
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- [\delta = \frac