n阶差分“中间点”的渐近性  被引量:2

Asymptotic Property of the Middle Point of n-th Order Difference

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作  者:马龙友[1] 寿玉亭[1] 刘长河[1] 张艳[1] 刘世祥[1] 

机构地区:[1]北京建筑工程学院,北京100044

出  处:《北京工业大学学报》2003年第1期73-78,共6页Journal of Beijing University of Technology

摘  要:对函数逼近论中等距节点和差分理论进行了研究,揭示了差分、差商与导数之间的联系;将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中,简明地推导出Lagrange差分中值定理等4个定理,并在此基础上对“中间点”的渐近性进行了研究,得出了一系列“中间点”的渐近性的结果,概括了有关文献对微分中值公式的“中间点”的渐近性的讨论;给出的引理改进了函数逼近论的证明方法,精简了函数逼近论中的一些内容。Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in 'differential mid-value are summarized. Some proof methods for theory of function approximation are improved by means of the given lemmas in this paper and some contents of theory of function approximation are simplified.

关 键 词:差分 渐近性 中间点 函数逼近论 等距节点 差商 导数 

分 类 号:O174.41[理学—数学]

 

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