Numerical error: Difference between revisions

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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 these simplifications usually involve the truncation of an infinite series expansion so as to make the computation possible and practical.

[[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]]).

==See also==

* [[Loss of significance]]

* [[numericalNumerical analysis]]

* [[Error analysis (mathematics)]]

* [[Round-off error]]

* [[Kahan summation algorithm]]

* [[Numerical sign problem]]

==References==

* ''Accuracy and Stability of Numerical Algorithms'', Nicholas J. Higham, ISBN {{isbn|0-89871-355-2}}

* "Computational Error And Complexity In Science And Engineering", V. Lakshmikantham, S.K. Sen, {{isbn|0444518606}}

[[Category:Computer arithmetic]]

[[Category:Numerical analysis]]

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