Higher order Jarratt-like iterations for solving systems of nonlinear equations

Жанлав, Т.; Otgondorj, Kh.

doi:10.1016/j.amc.2020.125849

Cited by 12 publications

(12 citation statements)

References 24 publications

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“…Jarrat's method has a convergence rate of four. Articles using Jarratt-like methods to solve SNEs can be found for example in [30,127,128].…”

Section: End Whilementioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

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This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications.To accomplish these objectives, we present a multi-part survey. In part one, we focus on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we will introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

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“…Jarrat's method has a convergence rate of four. Articles using Jarratt-like methods to solve SNEs can be found for example in [30,127,128].…”

Section: End Whilementioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…That simply means the number of significant digits double with the progress of each iteration. Numerous iterative techniques have been developed (see, for example [3,4,7,8,10,13,14,15,16,17], and references therein) to improve the convergence rate of the Newton's technique by introducing the additional functional or Jacobian evaluations. Evidently, Newton's technique utilizes a function evaluation (F ), a Jacobian matrix (F ′ ), and a matrix inversion (F ′−1 ) per iteration.…”

Section: Introductionmentioning

confidence: 99%

Simple and Efficient Fifth Order Solvers for Systems of Nonlinear Problems

Singh

Sharma

2023

Mathematical Modelling and Analysis

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In this study, two multi-step iterative techniques of fifth order convergence are explored to solve nonlinear equations. The techniques are designed with the prime objective of keeping the computational cost as low as possible. To claim this objective, the efficiency indices are determined and compared with the efficiencies of the existing techniques of same order. The outcome of comparison analysis is remarkable from the view of high computational efficiency of new methods. Performance and stability are illustrated by executing the numerical tests on some nonlinear problems of diverse nature. The entire analysis significantly favors the new techniques compared to their existing counterparts, especially for the case of large dimensional systems.

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“…In particular, we study the (local) convergence of the three-step scheme [33], given for each σ = 0, 1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

“…Other choices are given by ( 31), (32), and in paper [33]. Schemes (2) and (3) were shown to be of order (λ + 2) and 2j, respectively in [33], when T 1 = T 2 = R j , j = 1, 2, 3, . .…”

Section: Introductionmentioning

confidence: 99%

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Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences

et al. 2021

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Symmetries are important in studying the dynamics of physical systems which in turn are converted to solve equations. Jarratt’s method and its variants have been used extensively for this purpose. That is why in the present study, a unified local convergence analysis is developed of higher order Jarratt-type schemes for equations given on Banach space. Such schemes have been studied on the multidimensional Euclidean space provided that high order derivatives (not appearing on the schemes) exist. In addition, no errors estimates or results on the uniqueness of the solution that can be computed are given. These problems restrict the applicability of the methods. We address all these problems by using the first order derivative (appearing only on the schemes). Hence, the region of applicability of existing schemes is enlarged. Our technique can be used on other methods due to its generality. Numerical experiments from chemistry and other disciplines of applied sciences complete this study.

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Higher order Jarratt-like iterations for solving systems of nonlinear equations

Cited by 12 publications

References 24 publications

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Simple and Efficient Fifth Order Solvers for Systems of Nonlinear Problems

Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences

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