从近似值恢复精确值的一种改进算法
An Improved Algorithm for Recovering Exact Value from its Approximation
摘要：
数值近似计算可以快速解决大型复杂问题。它具有效率高的优点。然而，它只给出近似结果，而我们在许多领域需要精确的结果。近似计算与精确结果之间存在差距。Zhang建立了一座桥梁，当误差小于$1/((2N+2)(N-1)N)$时，用连分数方法从其近似值中恢复出一个精确有理数，其中$N$是有理数的分母绝对值的界。本文提出了一种改进的算法，该算法在误差小于$1/(4(N-1)N)$的情况下恢复出一个精确有理数。
英文摘要：
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between approximate computation and exact results. A bridge overriding the gap was built by Zhang, in which an exact rational number is recovered from its approximation by continued fraction method when the error is less than $1/((2N+2)(N-1)N)$, where $N$ is a bound on absolute value of denominator of the rational number. In this paper, an improved algorithm is presented by which a exact rational number is recovered when the error is less than $1/(4(N-1)N)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
