关于数值微分公式的两个注记

数学季刊 ›› 2012, Vol. 27 ›› Issue (4): 480-484.

关于数值微分公式的两个注记

School of Mathematics and Information Science, Nanchang Hangkong University

收稿日期:2010-10-15 出版日期:2012-12-30 发布日期:2023-03-13
作者简介:ZHENG Hua-sheng(1966-), male, native of Jingdezhen, Jiangxi, a professor of Nanchang Hangkong University, Ph.D., engages in numerical analysis and numerical solution of differential equations.
基金资助:
Supported by the Science and Technology Project of the Education Department of Jiangxi Province(GJJ08224 )； Supported by the Transformation of Education Project of the Education Department of Jiangxi Province(JxJG-09-7-28)

Two Notes on Numerical Differentiation Formulae

School of Mathematics and Information Science, Nanchang Hangkong University

Received:2010-10-15 Online:2012-12-30 Published:2023-03-13
About author: ZHENG Hua-sheng(1966-), male, native of Jingdezhen, Jiangxi, a professor of Nanchang Hangkong University, Ph.D., engages in numerical analysis and numerical solution of differential equations.
Supported by:
Supported by the Science and Technology Project of the Education Department of Jiangxi Province(GJJ08224 )； Supported by the Transformation of Education Project of the Education Department of Jiangxi Province(JxJG-09-7-28)

摘要/Abstract

摘要： Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper. In the first place, several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor’s formula. And then, based on the ideas of algebraic accuracy, several inverse problems of numerical differentiation formulae are given.

关键词: numerical differentiation, remainder term, asymptotic property, intermediate point, algebraic precision, inverse problem

Abstract: Some new conclusions on asymptotic properties and inverse problems of numerical differentiation formulae have been drawn in this paper. In the first place, several asymptotic properties of intermediate points of numerical differentiation formulae are presented by using Taylor’s formula. And then, based on the ideas of algebraic accuracy, several inverse problems of numerical differentiation formulae are given.

Key words: numerical differentiation, remainder term, asymptotic property, intermediate point, algebraic precision, inverse problem

中图分类号:

O241.4

郑华盛. 关于数值微分公式的两个注记[J]. 数学季刊, 2012, 27(4): 480-484.

ZHENG Hua-sheng. Two Notes on Numerical Differentiation Formulae[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(4): 480-484.

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