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| {{Other uses|Truncation error (numerical integration)}}
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| In [[numerical analysis]] and [[scientific computing]], '''truncation error''' is the error made by truncating an infinite sum and approximating it by a finite sum. For instance, if we approximate the [[sine]] function by the first two non-zero term of its Taylor series, as in <math>\sin(x) \approx x - \tfrac16 x^3</math> for small <math>x</math>, the resulting error is a truncation error. It is present even with infinite-precision arithmetic, because it is caused by truncation of the infinite [[Taylor series]] to form the algorithm.
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| Often, truncation error also includes [[discretization error]], which is the error that arises from taking a finite number of steps in a computation to approximate an infinite process. For example, in [[numerical methods for ordinary differential equations]], the continuously varying function that is the solution of the differential equation is approximated by a process that progresses step by step, and the error that this entails is a discretization or truncation error. See [[Truncation error (numerical integration)]] for more on this.
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| Occasionally, [[round-off error]] (the consequence of using finite precision [[Floating point | floating point numbers]] on computers) is also called truncation error, especially if the number is rounded by [[truncation]].
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| == References ==
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| * {{Citation | last1=Atkinson | first1=Kendall A. | title=An Introduction to Numerical Analysis | publisher=[[John Wiley & Sons]] | location=New York | edition=2nd | isbn=978-0-471-50023-0 | year=1989 | page=20 }}
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| * {{Citation | last1=Stoer | first1=Josef | last2=Bulirsch | first2=Roland | title=Introduction to Numerical Analysis | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=3rd | isbn=978-0-387-95452-3 | year=2002 | page=1 }}.
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| [[Category:Numerical analysis]]
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Latest revision as of 11:15, 11 December 2014
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