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]].

[[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.

* theThe first is referred to as [[Round-off error]] and is caused by the finite [[Precision (computer science)|precision]] of computations involving [[floating-point]] or integer valuesnumbers.

* theThe second, usually called truncation[[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.

==Measure==

Floating-point numerical error is often measured in ULP ([[unit in the last place]]).

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* [[Loss of significance]]

* [[Numerical analysis]]

* [[Error analysis (mathematics)]]

* [[Round-off error]]

* [[Kahan summation algorithm]]

* [[Impact of error]]

* [[Numerical sign problem]]