小数的最佳分数表示算法研究

计算机科学 ›› 2013, Vol. 40 ›› Issue (Z6): 354-355.

小数的最佳分数表示算法研究

薛丹,李顺东,杨宸

陕西师范大学计算机科学学院西安710062;陕西师范大学计算机科学学院西安710062;陕西师范大学计算机科学学院西安710062

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家自然科学基金(61070189,61272435,61170032)资助

Research on Best Fraction of Decimal

XUE Dan,LI Shun-dong and YANG Chen

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： 在科学与工程计算中无理数的表示与运算是一个非常棘手的问题。如果能够用整数表示无理数,将给科学与工程计算带来极大的方便。要实现无理数的整数化表示,第一步要做的是实现无理数的有理化表示。利用连分数作为桥梁,首先将无理数转化为连分数,然后根据计算精度的要求生成最简分数表示,从而实现无理数的最佳有理逼近。最后给出了一些常用常数在不同计算精度要求下的最佳有理逼近,其对科学计算有一定的指导意义。

关键词: 连分数,有理化,渐进分数,有理逼近,精确度

Abstract: In scientific computing,irrational operation is considerably intractable．Transform irrational into integer will greatly convenient in scientific computing．To achieve integer representation to irrational,the first step is to achieve rational representation to irrational．We first transform irrational into continued fraction by utilizing continued fractions technique．Secondly,it is possible and reasonable to choose the most concise expression of the fraction according to the accuracy demand,so that we can achieve the rational approximation of irrational number．A list of the simplest form and the approximation error of some commonly used computing constants under various accuracy requirements is given,which has guiding significance for scientific computing.

Key words: Continued fraction,Rationalization,Progressive score,Rational approximation,Accuracy

薛丹,李顺东,杨宸. 小数的最佳分数表示算法研究[J]. 计算机科学, 2013, 40(Z6): 354-355. https://doi.org/

XUE Dan,LI Shun-dong and YANG Chen. Research on Best Fraction of Decimal[J]. Computer Science, 2013, 40(Z6): 354-355. https://doi.org/

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