Add links to separate pages for roundoff and truncation error, move explanation for origin of "truncation" to Truncation error
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In [[software engineering]] and [[mathematics]], '''numerical error''' is the error in [[Numerical computation|the numerical computations]].
In [[software engineering]] and [[mathematics]], '''numerical error''' is the combined effect of two kinds of error in a calculation. The first is caused by the finite precision of computations involving [[floating-point]] or integer values. The second usually called truncation error is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation. The term truncation comes from the fact that either these simplifications usually involve the truncation of an [[infinite series]] expansion so as to make the computation possible and practical, or because the least significant bits of an arithmetic operation are thrown away.
[[File:Time series of the Tent map for the parameter m=2.0 which shows numerical error.svg|thumb|right|Time series of the [[Tent map]] for the parameter m=2.0 which shows numerical error: "the plot of time series (plot of x variable with respect to number of iterations) stops fluctuating and no values are observed after n=50". Parameter m= 2.0, initial point is random.]]
==Types==
It can be the combined effect of two kinds of error in a calculation.
The first is referred to as [[Round-off error]] and is caused by the finite [[Precision (computer science)|precision]] of computations involving [[floating-point]] numbers.
The second, usually called [[Truncation error]], is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.
==Measure==
Floating-point numerical error is often measured in ULP ([[unit in the last place]]).
Floating-point numerical error is often measured in ULP ([[unit in the last place]]).
==See also==
==See also==
* [[Loss of significance]]
* [[numerical analysis]]
* [[Numerical analysis]]
* [[Error analysis (mathematics)]]
* [[round-off error]]
* [[Round-off error]]
* [[Kahan summation algorithm]]
* [[Kahan summation algorithm]]
* [[Numerical sign problem]]
==References==
==References==
* ''Accuracy and Stability of Numerical Algorithms'', Nicholas J. Higham, ISBN 0-89871-355-2
* ''Accuracy and Stability of Numerical Algorithms'', Nicholas J. Higham, {{isbn|0-89871-355-2}}
* "Computational Error And Complexity In Science And Engineering", V. Lakshmikantham, S.K. Sen, ISBN 0444518606
* "Computational Error And Complexity In Science And Engineering", V. Lakshmikantham, S.K. Sen, {{isbn|0444518606}}
Time series of the Tent map for the parameter m=2.0 which shows numerical error: "the plot of time series (plot of x variable with respect to number of iterations) stops fluctuating and no values are observed after n=50". Parameter m= 2.0, initial point is random.
It can be the combined effect of two kinds of error in a calculation.
The first is referred to as Round-off error and is caused by the finite precision of computations involving floating-point numbers.
The second, usually called Truncation error, is the difference between the exact mathematical solution and the approximate solution obtained when simplifications are made to the mathematical equations to make them more amenable to calculation.
