Newton-Raphson Method: Overview and Applications

Sal Ly; Kim-Hung Pho; Shin-Hung Pan; Wing-Keung Wong

doi:10.47654/v28y2024i3p52-78

Authors

Sal Ly Faculty of Mathematics and Statistics, Ton Duc Thang University Ho Chi Minh City, Vietnam Author
Kim-Hung Pho Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam Author
Shin-Hung Pan Department of Information Management Chaoyang University of Technology, Taiwan Author
Wing-Keung Wong Department of Finance, Fintech Center, and Big Data Research Center, Asia University, Taiwan Corresponding Author

DOI:

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

Keywords:

Newton-Raphson method, Application, real problems, Mathematics

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.

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