不确定性的自动差异化:为第一个和更高的衍生品进行间隔计算差异化,并实现实现
Hend Dawood1, Nefertiti Megahed1
1Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
PeerJ. Computer science
|June 22, 2023
概括
本研究介绍了二次区间分化数的系统理论,使在不确定性下实现自动分化. 这种方法结合了间隔数学和算法差异化,以提高计算可靠性.
科学领域:
- 计算数学 计算数学 计算数学
- 间隔分析 间隔分析
背景情况:
- 在不确定性下获得可靠的知识在现代科学中至关重要.
- 间隔数学有效地处理不确定性和不精确性.
- 算法差异化比数值和符号方法具有优势.
研究的目的:
- 开发一个系统的二次区间分化数的理论.
- 在不确定性下处理一级和更高级自动衍生品.
- 通过使用间隔数学和算法差异化来扩展真实差异化算术.
主要方法:
- 微分区间代数的公理化.
- 对实函数和区间函数的区间扩展的定义.
- 开发一个关于区间分化算法的公理理论.
- 提出理论的断定性和一致性的证明.
主要成果:
- 开发的结构形成了一个多重非关联的S-semeniring.
- 在这个结构中的乘法被证明是次替代的和灵活的.
- 演示了间隔自动区分的计算实现.
结论:
- 提出的理论提供了一个强大的框架,用于在不确定性下自动区分.
- 这种方法增强了微分算法的功率和适用性.
- 该研究通过区间函数和实函数家族的例子说明了实际应用.
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