truncation error

　

WordNet

1. (mathematics) a miscalculation that results from cutting off a numerical calculation before it is finished
2. (baseball) a failure of a defensive player to make an out when normal play would have sufficed (同)misplay
3. departure from what is ethically acceptable (同)wrongdoing
4. (computer science) the occurrence of an incorrect result produced by a computer (同)computer error
5. a misconception resulting from incorrect information (同)erroneous belief
6. part of a statement that is not correct; "the book was full of errors" (同)mistake
7. the act of cutting short; "it is an obvious truncation of the verse"; "they were sentenced to a truncation of their limbs"
8. the replacement of an edge or solid angle (as in cutting a gemstone) by a plane (especially by a plane that is equally inclined to the adjacent faces)
9. to make a mistake or be incorrect (同)mistake, slip

PrepTutorEJDIC

1. 〈C〉『誤り』,『まちがい』 / 〈U〉思い違い,誤解 / 〈U〉〈C〉過ち,過失 / 〈U〉(計数の)誤差 / 〈C〉(野球で)エラー,失策
2. (判断・考え方・選択などで)『誤る』,まちがえる;過ちを犯す,罪を犯す《+『in』+『名』(do『ing』)》 / (正道・目的などから)それる,逸脱する《+『from』+『名』》

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2015/10/11 18:01:38」(JST)

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[Wiki en表示]

For other uses, see Truncation error (numerical integration).

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 for small , 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.

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.

Occasionally, round-off error (the consequence of using finite precision floating point numbers on computers) is also called truncation error, especially if the number is rounded by truncation.

References

• Atkinson, Kendall A. (1989), An Introduction to Numerical Analysis (2nd ed.), New York: John Wiley & Sons, p. 20, ISBN 978-0-471-50023-0 
• Stoer, Josef; Bulirsch, Roland (2002), Introduction to Numerical Analysis (3rd ed.), Berlin, New York: Springer-Verlag, p. 1, ISBN 978-0-387-95452-3 .

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Japanese Journal

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