English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 113648/144635 (79%)
Visitors : 51624206      Online Users : 552
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
    •  Adv. Search
    Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer Goto mobile version
    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/120115


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/120115


    Title: Linear Regression to Minimize the Total Error of the Numerical Differentiation
    Authors: 曾正男
    Tzeng, Jengnan
    Contributors: 應數系
    Date: 2017-11
    Issue Date: 2018-09-25 16:14:57 (UTC+8)
    Abstract: It is well known that numerical derivative contains two types of errors. One is truncation error and the other is rounding error. By evaluating variables with rounding error, together with step size and the unknown coefficient of the truncation error, the total error can be determined. We also know that the step size affects the truncation error very much, especially when the step size is large. On the other hand, rounding error will dominate numerical error when the step size is too small. Thus, to choose a suitable step size is an important task in computing the numerical differentiation. If we want to reach an accuracy result of the numerical difference, we had better estimate the best step size. We can use Taylor Expression to analyze the order of truncation error, which is usually expressed by the big O notation, that is, E(h) = Chk . Since the leading coefficient C contains the factor f (k)(ζ) for high order k and unknown ζ, the truncation error is often estimated by a roughly upper bound. If we try to estimate the high order difference f (k)(ζ), this term usually contains larger error. Hence, the uncertainty of ζ and the rounding errors hinder a possible accurate numerical derivative. We will introduce the statistical process into the traditional numerical difference. The new method estimates truncation error and rounding error at the same time for a given step size. When we estimate these two types of error successfully, we can reach much better modified results. We also propose a genetic approach to reach a confident numerical derivative.
    Relation: East Asian Journal on Applied Mathematics, Volume 7 Issue 4, pp. 810-826
    Data Type: article
    DOI 連結: https://doi.org/10.4208/eajam.161016.300517a
    DOI: 10.4208/eajam.161016.300517a
    Appears in Collections:[應用數學系] 期刊論文

    Files in This Item:

    File Description SizeFormat
    810826.pdf1336KbAdobe PDF2448View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback