An efficient fifth-order Steffensen-type method for solving systems of nonlinear equations

Singh, Anuradha

doi:10.1504/ijcsm.2018.095502

Cited by 12 publications

(13 citation statements)

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“…Recently, new parametric families of iterative methods were proposed in [2][3][4], including a fast procedure for solving this kind of problems. Also iterative methods avoiding the Jacobian matrix have been proposed in [5][6][7], with good orders of convergence. In them, Jacobian matrix F ′ (•) is replaced by [•, •; F ], the divided difference operator.…”

Section: Introductionmentioning

confidence: 99%

Several techniques for introducing memory in iterative processes to solve nonlinear systems

Cordero¹,

Garrido

Torregrosa³

et al. 2022

Preprint

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In this paper, we design two parametric classes of iterative methods without memory to solve nonlinear systems, whose convergence order is four and seven, respectively. From their error equations and to increase the convergence order without performing new functional evaluations, memory is introduced in these families of different forms. That allows us to increase from four to seven the convergence order in the first family and from seven to eleven in the second one. We perform some numerical experiments with big size systems for confirming the theoretical results and comparing the proposed methods along other known schemes.

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Section: Introductionmentioning

confidence: 99%

Several techniques for introducing memory in iterative processes to solve nonlinear systems

Cordero¹,

Garrido

Torregrosa³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, new parametric families of iterative methods were proposed in 2,3,4 , including a fast procedure for solving this kind of problems. Also iterative methods avoiding the Jacobian matrix have been proposed in 5,6,7 , with good orders of convergence. In them, Jacobian matrix 𝐹 ′ (⋅) is replaced by [⋅, ⋅; 𝐹 ], the divided difference operator.…”

Section: Introductionmentioning

confidence: 99%

Design of iterative methods with memory for solving nonlinear systems

Cordero

Garrido

Torregrosa

et al. 2022

Preprint

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“…In recent literature in this area of research, we can find other methods that reach higher orders (see, for example, previous studies [3][4][5][6][7] ), and they are designed by using different techniques like: Adomian decomposition, [8][9][10] multidimensional Steffensen-type schemes, [11][12][13][14][15][16] and weight function techniques. [17][18][19] Once a class of methods has been designed, it is interesting to carry out a multidimensional real dynamical study (see 20,21 ) in order to obtain the values most suitable of the parameters for setting stable schemes.…”

Section: Introductionmentioning

confidence: 99%

Isonormal surfaces: A new tool for the multidimensional dynamical analysis of iterative methods for solving nonlinear systems

Capdevila

Cordero

Torregrosa

2021

Math Methods in App Sciences

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The dynamical behavior of the rational vectorial operator associated with a multidimensional iterative method on polynomial systems gives us interesting information about the stability of the iterative scheme. The stability of fixed points, dynamic planes, bifurcation diagrams, etc. are known tools that provide us this information. In this manuscript, we introduce a new tool, which we call isonormal surface, to complement the information about the stability of the iterative method provided by the dynamical elements mentioned above. These dynamical instruments are used for analyzing the stability of a parametric family of multidimensional iterative schemes in terms of the value of the parameter. Some numerical tests confirm the obtained dynamical results.

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An efficient fifth-order Steffensen-type method for solving systems of nonlinear equations

Cited by 12 publications

References 0 publications

Several techniques for introducing memory in iterative processes to solve nonlinear systems

Several techniques for introducing memory in iterative processes to solve nonlinear systems

Design of iterative methods with memory for solving nonlinear systems

Isonormal surfaces: A new tool for the multidimensional dynamical analysis of iterative methods for solving nonlinear systems

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