Effective Subdivision Algorithm for Isolating Zeros of Real Systems of Equations, with Complexity Analysis
Effective Subdivision Algorithm for Isolating Zeros of Real Systems of Equations, with Complexity Analysis
复制标题
通过复杂性分析分离真实方程组零点的有效细分算法
DOI：
10.1145/3326229.3326270
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
C. Yap
中科院分区：
文献类型：
--
作者：
Juan Xu;C. Yap
我们描述了一种新算法miranda，用于隔离函数\ boldsymbolf的简单零：\ mathbbr ^n \ to \ mathbbr ^n在一个盒子B_0 \ subseteq \ subseteq \ mathbbr ^n中。功能\ BoldSymbolf及其部分衍生物必须具有间隔形式，但不必是多项式。我们的基于细分的算法是“有效的”，因为我们的算法描述还指定了数值精度，足以证明具有任何标准的BigFloat数字类型的实现。主要谓词是Moore-Kioustelidis（MK）测试，基于基于的，基于基于的测试，在Miranda的定理（1940年）上。根部分离算法。我们基于系统的固有几何参数提供了我们的算法。总体细分算法一般。
We describe a new algorithm Miranda for isolating the simple zeros of a function \boldsymbolf :\mathbbR ^n\to\mathbbR ^n within a box B_0\subseteq\mathbbR ^n. The function \boldsymbolf and its partial derivatives must have interval forms, but need not be polynomial. Our subdivision-based algorithm is "effective'' in the sense that our algorithmic description also specifies the numerical precision that is sufficient to certify an implementation with any standard BigFloat number type. The main predicate is the Moore-Kioustelidis (MK) test, based on Miranda's Theorem (1940). Although the MK test is well-known, this paper appears to be the first synthesis of this test into a complete root isolation algorithm. We provide a complexity analysis of our algorithm based on intrinsic geometric parameters of the system. Our algorithm and complexity analysis are developed using 3 levels of description (Abstract, Interval, Effective). This methodology provides a systematic pathway for achieving effective subdivision algorithms in general.
DOI：
10.1007/978-3-319-96418-8_28
发表时间：
2018
期刊：
International Congress on Mathematical Software (ICMS
影响因子：
--
作者：
Imbach, Rémi;Pan, Victor;Yap, Chee
通讯作者：
Yap, Chee
影响因子：
0.7
作者：
Sagraloff, Michael;Mehlhorn, Kurt
通讯作者：
Mehlhorn, Kurt