Newton-Raphson Method: Overview and Applications

Sal Ly, Kim-Hung Pho, Shin-Hung Pan and Wing-Keung Wong
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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

Advances in Decision Sciences, 2024, vol. 28, issue 3, 52-78

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.

Keywords: Newton-Raphson method; Application; real problems; Mathematics. (search for similar items in EconPapers)
JEL-codes: A10 G00 G31 O32 (search for similar items in EconPapers)
Date: 2024
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