数值计算中的外推算法
摘要
本文主要介绍和讨论数值积分与数值微分中的外推法的基本理论与应用。并以 的计算为例，利用数值积分通过编写VC++程序求出 的近似值。在数值积分计算中,我们通过特殊的函数来逼近f(x),使得用特殊函数的积分来近似代替原函数的积分.。对于数值微分，我们通过导出1个渐近展开式，利用外推法，得到数值微分的高精度计算公式。为了减小误差，我们采用误差分析法、误差补偿的方法得到更好的结果。本文从积分运算的各种优化模型中逐渐推导出外推法，并且着重从误差的角度分析外推法的优劣。鉴于外推法应用的广泛性和VC++的通用性和高可视性，在理论分析得出算法后笔者用VC++实现T数表和精度控制。
关键词：外推法；数值微分；数值积分；高精度; VC++.
Extrapolation Method in Numerical Computations
Abstract: In this paper, the application of the extrapolation of and the numerical integration and numerical differential are mainly discussed. Extrapolation method in visual C ++ also be discussed .The basic idea of all the methods for numerical integration is approaching f(x) through a kind of special function whose integral can approximately replace the integral of the primitive function. By deducing an asymptotic expansion for numerical integration, a high accuracy algorithm is proposed by extrapolation method. In order to decrease the error, we use error analyzing method and error compensate will receive a better result. This text optimize from total mark various kinds of operation model is it appear law of extrapolating to derive gradually, is it extrapolate quality of law to analyse in terms of error emphatically , extrapolate law use very extensive with visture C ++ commonability and high visuality of language, in theory analyse draw algorithm realize with VC++ T count form and precision control.
Keywords: extrapolation method, numerical integration, numerical differentiation, high accuracy algorithm. visual C++ (VC++).