[星光大道]肩上芭蕾《九儿》 表演：李梦楠
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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 |
In [[software engineering]] and [[mathematics]], '''numerical error''' is the error in [[Numerical computation|the numerical computations]]. |
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[[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.]] |
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==Types== |
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It can be the combined effect of two kinds of error in a calculation. |
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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. |
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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. |
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==Measure== |
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==See also== |
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* [[Loss of significance]] |
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* [[Numerical analysis]] |
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* [[Error analysis (mathematics)]] |
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* [[Round-off error]] |
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* [[Kahan summation algorithm]] |
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* [[Numerical sign problem]] |
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==References== |
==References== |
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Accuracy and Stability of Numerical Algorithms |
* ''Accuracy and Stability of Numerical Algorithms'', Nicholas J. Higham, {{isbn|0-89871-355-2}} |
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* "Computational Error And Complexity In Science And Engineering", V. Lakshmikantham, S.K. Sen, {{isbn|0444518606}} |
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[[Category: |
[[Category:Computer arithmetic]] |
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{{applied-math-stub}} |
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Latest revision as of 01:08, 13 February 2025
In software engineering and mathematics, numerical error is the error in the numerical computations.
Types
[edit]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.
Measure
[edit]Floating-point numerical error is often measured in ULP (unit in the last place).
See also
[edit]- Loss of significance
- Numerical analysis
- Error analysis (mathematics)
- Round-off error
- Kahan summation algorithm
- Numerical sign problem
References
[edit]- 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
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