Approximation error - Definition and Overview

In the mathematical subfield of numerical analysis the approximation error in some data is the difference between the exact value and the value used. An approximation error can occur because

1. the measurement of the data is not precise (due to the instruments)
2. we use an approximation instead of the real data (e.g. 3.14 instead of π)

One commonly distinguishes between the relative error and the absolute error.

The numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.

Definition

Given some value a and an approximation b the absolute error is

<math>\epsilon := a - b<math>

and the relative error is

<math>\eta := \frac{a - b}{a} <math>