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代数数极小多项式的近似重构 被引量：2

RECONSTRUCTING MINIMAL POLYNOMIAL FROM APPROXIMATE ALGEBRAIC NUMBERS
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摘要 给出了代数数极小多项式近似重构的误差控制条件,进而基于同步整数关系探测算法SIRD,得到一个从代数数近似值重构其准确极小多项式的完备的新算法,从而将"采用近似计算获得准确值"这一思想的适用范围从有理数扩展到代数数. This paper gives an error condition for reconstructing the minimal polynomial of an algebraic number from its approximation, and then present a newly complete algorithm to obtain the exact minimal polynomial from an approximate value by simultaneous integer rela- tions detection. This work extends the applicable area of ＂obtaining exact value by approximate computations＂ from the rational to algebraic numbers.
作者 陈经纬 冯勇 秦小林 张景中
机构地区 中国科学院重庆绿色智能技术研究院 中科院成都计算机应用研究所 中国科学院研究生院
出处 《系统科学与数学》 CSCD 北大核心 2011年第8期903-912,共10页 Journal of Systems Science and Mathematical Sciences
基金 国家973计划资助(2011CB302400) 国家自然科学基金资助(10771205) 中国科学院知识创新基金(KJCX2-YW-S02)资助 中国科学院西部之光项目资助
关键词 同步整数关系 代数数 极小多项式. Simultaneous integer relation, algebraic number, minimal polynomial.
分类号 O174.14 [理学—基础数学]
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共引文献6

同被引文献16

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系统科学与数学
2011年 第8期

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