Approximation error ( $x_{approx} - x$ )

For a numerical reference value

x

and a computed value

x_{approx}

, the signed approximation error is

x_{approx} - x

. Stating the reference matters: comparison with a measured value assesses agreement with that value, rather than with an unknown exact value.

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Approximation error refers to the difference between a value produced by an approximate method and the exact or true value that one is trying to estimate or calculate. In various fields such as mathematics, statistics, computer science, and engineering, approximation errors occur when simplified models, numerical methods, or algorithms are used to estimate more complex systems or functions.

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