Comparative study of methods of various orders for finding repeated roots of nonlinear equations

Chun, Changbum; Neta, Beny

doi:10.1016/j.cam.2018.02.009

Cited by 12 publications

(9 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the last decade, many papers appeared using the idea of basin of attraction to compare the efficiency of many methods. See, for example, Chun and Neta [13,14] and references there.…”

Section: Dynamics Study Of the Methodsmentioning

confidence: 99%

A New Derivative-Free Method to Solve Nonlinear Equations

Neta

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the last decade, many papers appeared using the idea of basin of attraction to compare the efficiency of many methods. See, for example, Chun and Neta [13,14] and references there.…”

Section: Dynamics Study Of the Methodsmentioning

confidence: 99%

A New Derivative-Free Method to Solve Nonlinear Equations

Neta

2021

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Today, dynamics study of root-finding methods with polynomiography is an essential part of modern analysis of the quality of these methods [ 28 ]. It turns out that this form of dynamics study is a powerful tool in selecting optimal parameters that appear in the iterative methods for solving non-linear equations and to compare these methods [ 29 , 30 ]. The visualisation methods proposed in the work will also be called polynomiography because of their similarity to the primary polynomiography, despite the fact that we use any functions, not just polynomials.…”

Section: Introductionmentioning

confidence: 99%

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

Gościniak

Gdawiec

2020

Entropy

View full text Add to dashboard Cite

There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm’s elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm’s operation allow to understand the influence of the proposed modifications on the algorithm’s behaviour. Understanding the impact of the proposed modification on the algorithm’s operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications.

show abstract

“…In the last decade many papers appeared using the idea of basin of attraction to compare the efficiency of many methods. See, for example, Chun and Neta [2], [3] and references there.…”

Section: Introductionmentioning

confidence: 99%