New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations

Narang, Mona; Bhatia, Saurabh; Kanwar, V.

doi:10.1016/j.amc.2015.11.063

Cited by 20 publications

(23 citation statements)

References 15 publications

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“…The main purpose of this combined approach is to accelerate the rate of convergence and to obtain the local convergence. Narang et al [19] presented a fourth order two parameter Chebyshev-Halley like twopoint family for solving the nonlinear equations of large-scale systems. Saheya et al [20] presented an improved Newton method based on iterative rational approximation model.…”

Section: *Corresponding Authormentioning

confidence: 99%

A new iterative linearization approach for solving nonlinear equations systems

Temelcan

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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Nonlinear equations arise frequently while modeling chemistry, physics, economy and engineering problems. In this paper, a new iterative approach for finding a solution of a nonlinear equations system (NLES) is presented by applying a linearization technique. The proposed approach is based on computational method that converts NLES into a linear equations system by using Taylor series expansion at the chosen arbitrary nonnegative initial point. Using the obtained solution of the linear equations system, a linear programming (LP) problem is constructed by considering the equations as constraints and minimizing the objective function constructed as the summation of balancing variables. At the end of the presented algorithm, the exact solution of the NLES is obtained. The performance of the proposed approach has been demonstrated by considering different numerical examples from literature.

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Section: *Corresponding Authormentioning

confidence: 99%

A new iterative linearization approach for solving nonlinear equations systems

Temelcan

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…In quest of efficient higher order method, a number of improved, multipoint Newton's or Newton-like iterative schemes have been proposed in literature; see, for example [3,5,[8][9][10][12][13][14][15][16][17][18][19] and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Local Convergence of an Efficient Multipoint Iterative Method in Banach Space

2020

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We discuss the local convergence of a derivative-free eighth order method in a Banach space setting. The present study provides the radius of convergence and bounds on errors under the hypothesis based on the first Fréchet-derivative only. The approaches of using Taylor expansions, containing higher order derivatives, do not provide such estimates since the derivatives may be nonexistent or costly to compute. By using only first derivative, the method can be applied to a wider class of functions and hence its applications are expanded. Numerical experiments show that the present results are applicable to the cases wherein previous results cannot be applied.

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“…, (2) which has a quadratic order of convergence. In order to achieve higher convergence order, a number of modified, multistep Newton's or Newton-type iterations have been developed in the literature; see [3,4,6,7,[9][10][11][12][15][16][17][18][19] and references cited therein. There is another important class of multistep methods based on Jarratt methods or Jarratt-type methods [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Local Convergence and Attraction Basins of Higher Order, Jarratt-Like Iterations

2019

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We studied the local convergence of a family of sixth order Jarratt-like methods in Banach space setting. The procedure so applied provides the radius of convergence and bounds on errors under the conditions based on the first Fréchet-derivative only. Such estimates are not proposed in the approaches using Taylor expansions of higher order derivatives which may be nonexistent or costly to compute. In this sense we can extend usage of the methods considered, since the methods can be applied to a wider class of functions. Numerical testing on examples show that the present results can be applied to the cases where earlier results are not applicable. Finally, the convergence domains are assessed by means of a geometrical approach; namely, the basins of attraction that allow us to find members of family with stable convergence behavior and with unstable behavior.

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New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations

Cited by 20 publications

References 15 publications

A new iterative linearization approach for solving nonlinear equations systems

A new iterative linearization approach for solving nonlinear equations systems

Local Convergence of an Efficient Multipoint Iterative Method in Banach Space

Local Convergence and Attraction Basins of Higher Order, Jarratt-Like Iterations

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