A new family of Newton-type iterative methods with and without memory for solving nonlinear equations

Wang, Xiaofeng; Zhang, Tie

doi:10.1007/s10092-012-0072-2

Cited by 31 publications

(25 citation statements)

References 10 publications

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“…This method is compared with methods XW41 (16)(17)(18), XW42 (16)(17)(18)(19), XW43 (16)(17)(18)(19)(20), XW44 (17)(18), XW45 (17)(18)(19), and XW46 (17)(18)(19)(20) presented in [5], XW5 (18)(19)(20)(21)(22)(23)(24) given in [1], method SK7 in [29], and methods XW81 (37-34), XW82 (37-35), XW83 (37-36), XW84 (38-34), XW85 (38-35), and XW86 (38-36) given in [6] by using the test functions shown in Table 1.…”

Section: Numerical Comparisonmentioning

confidence: 99%

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Dynamical Techniques for Analyzing Iterative Schemes with Memory

Choubey¹,

Cordero

Jaiswal

et al. 2018

Complexity

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We construct a new biparametric three-point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self-accelerating parameters, we have modified an existing seventh-order method. The parameters have been defined by Hermite interpolating polynomial that allows the accelerating effect. In particular, the R-order of the proposed iterative method with memory is increased from seven to ten. A real multidimensional analysis of the stability of this method with memory is made, in order to study its dependence on the initial estimations. Taking into account that usually iterative methods with memory are more stable than their derivative-free partners and the obtained results in this study, the behavior of this scheme shows to be excellent, but for a small domain. Numerical examples and comparison are also provided, confirming the theoretical results.

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Section: Numerical Comparisonmentioning

confidence: 99%

“…In this direction, numerous iterative methods have been projected (see, e.g., [1][2][3][4][5][6][7]). These iterative methods have a noteworthy area of research in numerical analysis, as they can be applied in several areas of pure or applied sciences.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Techniques for Analyzing Iterative Schemes with Memory

Choubey¹,

Cordero

Jaiswal

et al. 2018

Complexity

View full text Add to dashboard Cite

show abstract

“…Using interpolation method to construct self-accelerating parameter, we [4][5][6] obtained some self-accelerating type methods, one of them is given by…”

Section: Introductionmentioning

confidence: 99%

A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter

Wang

Fan

2020

Mathematics

Self Cite

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In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order of new method is 2 + 6 ≈ 4.4495 . Numerical experiments are made to show the performance of the new method, which supports the theoretical results.

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“…Since 1960's, many iterative methods have been proposed for solving nonlinear equations, see [1][2][3][4][5] and the references therein. Specifically, Wang and Zhang in [1] developed the following iterative method 2 1 ( ) , ( ) …”

Section: Introductionmentioning

confidence: 99%