数字函数微分算法误差分析
Error Analysis for Differential Algorithm of Digital Function Generation
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摘要: 在数字函数发生方法中,微分算法和齐田法形式不同,但就它们的基本特点及发生函数时 的误差而言,两者并没有重要的区别.微分法发生的曲线与给定函数之间的误差包括基本误 差和走步误差.基本误差系微分法发生曲线时实际逼近的函数(称为逼近函数)与给定函数 间的误差.逼近函数可以从给定的函数导出.走步误差为微分法发生曲线与逼近函数间因步 法不同而产生的误差.本文证明了用微分法发生二阶、三阶函数时的基本误差相当大,走步误 差比基本误差要小得多.Abstract: In methods of function genration, DDA and SFT (SAITA function generation) nave quite different forms, although their basic characteristics and errors of function generatio,n have no major differences. The errors between a curve generated by differential algorithm and its original given function consists of basic error and stepping error. A function generated by a differential algorithm approximates a function (properly called an approximate 'function) which deviates from its original function. This error is called "basic error". The approximated function can be derived from the given function itself. Curves generated by differential algorithm may also more or less deviate from their approximated function owing to different stepping approaches. This causes "stepping error". Analysis for polynomial functions of the second and third order shows that deviation of approximatd functions from their given functions may be quite significant. The stepping error is generally much smaller than that of basic errors.
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