一种关于~pc(0≤c<1)的快精算法  

A New Fast and Accurate Approach for Computing ~pc(0≤c<1)

作　　者：贺跃[1] 郑建军[2] 管琰平[1] 

机构地区：[1]北京理工大学信息科学技术学院,北京100081 [2]北京理工大学管理与经济学院,北京100081

出　　处：《火力与指挥控制》2005年第8期86-87,共2页Fire Control & Command Control

摘　　要：求pc(p>1,正整数)的值时,若c较小,通常会存在收敛速度较慢以及数值字长有限所致精度变差的问题。提出了一种关于pc(0≤c<1)的快精算法,该方法按照定点二进制数特点,通过适当扩大c值,利用牛顿迭代法求取近似值,在采用选值法确定初值时,将对应值域分为若干等间隔子区间,初值精度取决于间隔h的大小,而h的大小则根据迭代精度和预定迭代次数确定,由此可获得高精度初值,从而在理论上使pc的迭代计算达到快速、高精度的目的。To work out a correct solution to p√c （p〉 1, positive integer） when c is less, some problems usually be lied, such as convergence speed is rather slow and the accuracy with finite numerical value length is depressed. A new fast and accurate approach is proposed for computing p√c（0≤c〈1）, according to the characteristic of fixed-point binary digit, that properly enlarges the value of c in order to get the approximation by Newton iterative method. When ascertaining the initial value by the pick-value method, the corresponding value region is divided into some equal-internal child spaces, and the accuracy of the initial value is lied on the interval h, that is ascertained based on the iterative accuracy and the iterative pre-times, then the initial value can have high accuracy, and the iterative calculation about p√c could be fast and have high accuracy in theory.

关 键 词：牛顿迭代法 定点二进制数 数值分析 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]