One-Point Optimal Family of Multiple Root Solvers of Second-Order Article Swipe

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Deepak Kumar , Janak Raj Sharma , Clemente Cesarano ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.3390/math7070655

This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of nonlinear equations, and is based on the procedure of weight functions. The convergence behavior is discussed by showing some essential conditions of the weight function. The well-known modified Newton method is a member of the proposed family for particular choices of the weight function. The dynamical nature of different members is presented by using a technique called the “basin of attraction”. Several practical problems are given to compare different methods of the presented family.

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Mathematics

Newton's Method

Mathematical Analysis

Concepts

Mathematics Conjecture Convergence (economics) Weight function Root (linguistics) Function (biology) Order (exchange) Applied mathematics Point (geometry) Nonlinear system Newton's method Root-finding algorithm Mathematical optimization Mathematical analysis Pure mathematics Geometry Evolutionary biology Finance Philosophy Economics Economic growth Physics Biology Quantum mechanics Linguistics

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Type: article
Language: en
Landing Page: https://doi.org/10.3390/math7070655
PDF: https://www.mdpi.com/2227-7390/7/7/655/pdf?version=1563878293
OA Status: gold
Cited By: 5
References: 38
Related Works: 10
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DOI: https://doi.org/10.3390/math7070655

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Title: One-Point Optimal Family of Multiple Root Solvers of Second-Order

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Language: en

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Publication year: 2019

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Publication date: 2019-07-21

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Authors: Deepak Kumar, Janak Raj Sharma, Clemente Cesarano

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Landing page: https://doi.org/10.3390/math7070655

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Concepts: Mathematics, Conjecture, Convergence (economics), Weight function, Root (linguistics), Function (biology), Order (exchange), Applied mathematics, Point (geometry), Nonlinear system, Newton's method, Root-finding algorithm, Mathematical optimization, Mathematical analysis, Pure mathematics, Geometry, Evolutionary biology, Finance, Philosophy, Economics, Economic growth, Physics, Biology, Quantum mechanics, Linguistics

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Cited by: 5

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Citations by year (recent): 2023: 4, 2020: 1

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