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Newton-Raphson Method Overview and Applications

Newton-Raphson Method Overview and Applications

Title

Newton-Raphson Method: Overview and Applications

Authors

  • 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.
Findings: The findings of this paper include a detailed examination of the NRM, demonstrating its efficacy in solving non-linear equations, systems of equations, and optimization problems. The study further highlights the relevance of NRM in addressing complex challenges within probability, statistics, applied mathematics, and other related fields.
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.

Keywords

Newton-Raphson method, Application, real problems, Mathematics.

Classification-JEL

A10, G00, G31, O32

Pages

52-78

How to Cite

Sal Ly, Kim-Hung Pho, Shin-Hung Pan, & Wong, W.-K. (2025). Newton-Raphson Method: Overview and Applications. Advances in Decision Sciences, 28(3), 52-78.

https://doi.org/10.47654/v28y2024i3p52-78

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ISSN 2090-3359 (Print)
ISSN 2090-3367 (Online)

Asia University, Taiwan

Scientific and Business World

4.7
2023CiteScore
 
86th percentile
Powered by  Scopus
SCImago Journal & Country Rank
Q2 in Scopus
CiteScore 2023 = 4.7
CiteScoreTracker 2024 = 8.5
SNIP 2023 = 0.799
SJR Quartile = Q1
SJR 2024 = 0.814
H-Index = 20

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