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Newton-Raphson Method: Overview and Applications

Author

Listed:
  • Sal Ly

    (Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • Kim-Hung Pho

    (Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam)

  • Shin-Hung Pan

    (Department of Information Management, Chaoyang University of Technology, Taiwan)

  • Wing-Keung Wong

    (Department of Finance, Fintech Center, and Big Data Research Center, Asia University, Taiwan, and Department of Medical Research, China Medical University Hospital, Taiwan, and Department of Economics and Finance, the Hang Seng University of Hong Kong, Hong Kong)

Abstract

[Purpose] This paper provides a comprehensive overview of the Newton-Raphson method (NRM) and illustrates the use of the theory by applying it to diverse scientific fields. [Design/methodology/approach] This study employs a systematic approach to analyze the key characteristics of the NRM that facilitate its broad applicability across numerous scientific disciplines. We thoroughly explore its mathematical foundations, computational advantages, and practical implementations, emphasizing its versatility as a problem-solving tool. [Originality/value] This study contributes to the existing literature by providing a comprehensive and in-depth analysis of the NRM’s diverse applications. It effectively bridges the gap between theoretical understanding and practical utilization, thereby serving as a valuable resource for researchers and practitioners seeking to leverage the NRM in their respective domains. [Practical Implications] This research showcases the practical utility of the NRM through two illustrative case studies: optimizing loudspeaker placement for COVID-19 public health communication and determining the submersion depth of a floating spherical object in water. Additionally, the paper demonstrates the NRM’s extensive use in estimating parameters of probability distributions and regression models. It highlights its significance across various areas within Decision Sciences, including applied mathematics, finance, and education. This paper contributes both a theoretical overview and a display of diverse practical applications of the NRM.

Suggested Citation

  • Sal Ly & Kim-Hung Pho & Shin-Hung Pan & Wing-Keung Wong, 2024. "Newton-Raphson Method: Overview and Applications," Advances in Decision Sciences, Asia University, Taiwan, vol. 28(3), pages 52-78, September.
    • Handle: RePEc:aag:wpaper:v:28:y:2024:i:3:p:52-78
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    References listed on IDEAS

    as
    1. T. Martin Lukusa & Shen-Ming Lee & Chin-Shang Li, 2016. "Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 457-483, May.
    2. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    3. Buu-Chau Truong & Nguyen Van Thuan & Nguyen Huu Hau & Michael McAleer, 2019. "Applications of the Newton-Raphson Method in Decision Sciences and Education," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(4), pages 52-80, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Newton-Raphson method; Application; real problems; Mathematics.;
    All these keywords.

    JEL classification:

    • A10 - General Economics and Teaching - - General Economics - - - General
    • G00 - Financial Economics - - General - - - General
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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