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Derek farn (talk | contribs) Two kinds of truncation error |
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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 |
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. |
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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]]). |
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Revision as of 11:08, 17 December 2008
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.
Floating-point numerical error is often measured in ULP (unit in the last place).
See also
References
- Accuracy and Stability of Numerical Algorithms, Nicholas J. Higham, ISBN 0-89871-355-2
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