Dynamics of iterative families with memory based on weight functions procedure

Chicharro, Francisco Israel; Cordero, Alicia; Torregrosa, Juan R.

doi:10.1016/j.cam.2018.01.019

Cited by 17 publications

(23 citation statements)

References 19 publications

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“…In this section, we proposed a new three-point extension of King's method [18][19][20][21] having sixth-order convergence. For this purpose, we consider the well-known fourth-order King's method, which is given by…”

Section: Design Of the King's Family For Multidimensional Casementioning

confidence: 99%

Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations

2019

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We present a three-step family of iterative methods to solve systems of nonlinear equations. This family is a generalization of the well-known fourth-order King’s family to the multidimensional case. The convergence analysis of the methods is provided under mild conditions. The analytical discussion of the work is upheld by performing numerical experiments on some application oriented problems. Finally, numerical results demonstrate the validity and reliability of the suggested methods.

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Section: Design Of the King's Family For Multidimensional Casementioning

confidence: 99%

Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations

2019

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“…Method (3) is defined as MWM in this paper. Many efficiency iterative methods with memory have been studied in recent years, see [4][5][6][7][8][9][10]. Most of them achieved higher convergence order by using the self-accelerating parameters.…”

Section: Introductionmentioning

confidence: 99%

A New Newton Method with Memory for Solving Nonlinear Equations

Wang

Tao

2020

Mathematics

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A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant parameter of Newton method without memory by a variable self-accelerating parameter, we obtain a novel Newton method with memory. The convergence order of the new Newton method with memory is 1 + 2 . The acceleration of the convergence rate is attained without any additional function evaluations. The main innovation is that the self-accelerating parameter is constructed by a simple way. Numerical experiments show the presented method has faster convergence speed than existing methods.

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“…In this work, we focus on the order of convergence of two Traub-type methods when we modify its iterative expression to obtain methods with memory. Moreover, the dynamical analysis is performed in a similar way as done in [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Impact on Stability by the Use of Memory in Traub-Type Schemes

et al. 2020

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In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub’s method, they have been designed using linear approximations or the Newton’s interpolation polynomials. In both cases, the parameters use information from the current and the previous iterations, so they define a method with memory. Moreover, they achieve higher order of convergence than Traub’s scheme without any additional functional evaluations. The real dynamical analysis verifies that the proposed methods with memory not only converge faster, but they are also more stable than the original scheme. The methods selected by means of this analysis can be applied for solving nonlinear problems with a wider set of initial estimations than their original partners. This fact also involves a lower number of iterations in the process.

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Dynamics of iterative families with memory based on weight functions procedure

Cited by 17 publications

References 19 publications

Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations

Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations

A New Newton Method with Memory for Solving Nonlinear Equations

Impact on Stability by the Use of Memory in Traub-Type Schemes

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