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11hours

铜虫 (小有名气)

[求助] 什么是 first order approximation?

first order approximation 是什么意思?第一近似么?麻烦详细解释一下。
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11hours

铜虫 (小有名气)

wbcui: 我帮你给了 2011-12-07 19:17:33
维基 order of approximation
In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more refined approximations: in increasing order of precision, a zeroth order approximation, a first order approximation, a second order approximation, and so forth.

Formally, an nth order approximation is one where the order of magnitude of the error is at most xn, or in terms of big O notation, the error is O(xn). In suitable circumstances, approximating a function by a Taylor polynomial of degree n yields an nth order approximation, by Taylor's theorem: a first order approximation is a linear approximation, and so forth.
6楼2011-12-07 12:32:26
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shecf

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小木虫--警长

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语境,那里见到的?
业精于勤荒于嬉,行成于思而毁于随!
2楼2011-12-07 11:04:44
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11hours

铜虫 (小有名气)

11hours: 回帖置顶 2011-12-07 11:30:47
引用回帖:
2楼: Originally posted by shecf at 2011-12-07 11:04:44:
语境,那里见到的?

文献 《Numerical Analysis of Hydrogen Transport Near a Blunting Crack Tip》
作者 P.Sofronis 等
语境
讨论H扩散通量势函数中应力势函数部分。应力部分的势函数等于平均应力乘以H偏摩尔体积。下面跟的这一句“the assumption of dilational distortion is known to be correct to a first order approximation (Hirth, 1977 )”
3楼2011-12-07 11:21:13
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aduyuandu

银虫 (小有名气)

【答案】应助回帖

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11hours(金币+2): 就是一阶近似 2011-12-07 12:30:39
wbcui(金币+3): 多谢参与 2011-12-07 19:17:10
引用回帖:
3楼: Originally posted by 11hours at 2011-12-07 11:21:13:
文献 《Numerical Analysis of Hydrogen Transport Near a Blunting Crack Tip》
作者 P.Sofronis 等
语境
讨论H扩散通量势函数中应力势函数部分。应力部分的势函数等于平均应力乘以H偏摩尔体积。下面跟的这一 ...

是不是这个意思 函数在某点处用级数形式展开 忽略高次项而做的近似
4楼2011-12-07 11:26:07
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