纳皮尔对数的数学证明及精度分析
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1.百度自动驾驶技术部;2.百度技术管理部;3.北京师范大学系统科学学院;4.中国科学院深圳先进技术研究院

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Proof of Napier’s log and Analysis of Precision
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1.Department of Autonomous Driving Technology, Baidu Inc.;2.Department of Technology Management, Baidu Inc.;3.School of Systems Science, Beijing Normal University;4.Shenzhen Institute of Advanced Technology CAS, Shenzhen

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    摘要:

    对数函数在自动驾驶系统中有着广泛应用,如自动驾驶感知系统通常采用的深度学习方法中,卷积神经网络常会利用对数函数来设计损失函数,故研究对数发明的历史对于掌握对数的概念和应用具有重要意义。本文阐述了纳皮尔对数的定义及其三张表,分析了前人的两类证明方法,提出了新的基于指数函数构造的证明方法。同时本文还分析了纳皮尔的计算方法,相比于对照方法,给出了纳皮尔对精度范围的优化结果,通过MPRF库进行了计算,结果表明纳皮尔对数计算结果更接近真实值。

    Abstract:

    In the automatic driving systems, logarithm function has been widely used. For example, logarithm function is often used to design loss function in deep learning or convolutional neural network, which serves as the basis for the automatic driving perception system. Therefore, studying the history of invention of logarithm is of great significance to master the concept and application. This paper studies the definition of Napier""s logarithm and his three tables, analyzes two kinds of proof methods of predecessors, and puts forward new proof methods based on the exponential function. Meanwhile, this paper also analyzes Napier""s calculation method. Compared with other alternative methods, the optimization results of Napier""s interval approximation are given. The calculation by MPRF library shows that Napier""s method is more convergent to the true value.

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引用本文

孙鹏,王云鹏,吴琼,等.纳皮尔对数的数学证明及精度分析 [J].集成技术,

Citing format
SUN Peng, WANG Yunpeng, WU Qiong, et al. Proof of Napier’s log and Analysis of Precision[J]. Journal of Integration Technology.

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历史
  • 收稿日期:2023-08-17
  • 最后修改日期:2023-08-17
  • 录用日期:2023-11-21
  • 在线发布日期: 2023-11-23
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