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::Approximation error

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{{#invoke:broader|broader}}

Graph of <math>f(x) = e^x</math> (blue) with its linear approximation <math>P_1(x) = 1 + x</math> (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0.

The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because

  1. the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5 cm but since the ruler does not use decimals, you round it to 5 cm.) or
  2. approximations are used instead of the real data (e.g., 3.14 instead of π).

In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.


Approximation error sections
Intro  Formal Definition  Examples  Uses of relative error  Instruments  See also  References  External links  

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Error::value    Relative::absolute    Error'''::approx    Scale::example    Exact::analysis    Would::percent

{{#invoke:broader|broader}}

Graph of <math>f(x) = e^x</math> (blue) with its linear approximation <math>P_1(x) = 1 + x</math> (red) at a = 0. The approximation error is the gap between the curves, and it increases for x values further from 0.

The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because

  1. the measurement of the data is not precise due to the instruments. (e.g., the accurate reading of a piece of paper is 4.5 cm but since the ruler does not use decimals, you round it to 5 cm.) or
  2. approximations are used instead of the real data (e.g., 3.14 instead of π).

In the mathematical field of numerical analysis, the numerical stability of an algorithm in numerical analysis indicates how the error is propagated by the algorithm.


Approximation error sections
Intro  Formal Definition  Examples  Uses of relative error  Instruments  See also  References  External links  

PREVIOUS: IntroNEXT: Formal Definition
<<>>