Numerical error: Difference between revisions

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In [[software engineering]] and [[mathematics]], '''numerical error''' is the name given to two kinds of error that occur in a calculation. The first is caused by[[Numerical computation|the finite precision ofnumerical computations involving [[floating-point]]. values and the second (sometimes called the ''theoretical 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.

[[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 ([[Unitunit in the Lastlast Placeplace]]).

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 by'', 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:MathematicsComputer arithmetic]]

[[Category:Software engineering]]

[[Category:Arithmetic]]

[[Category:Numerical analysis]]

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