2017
DOI: 10.1016/j.amc.2017.07.051
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Higher-order derivative-free families of Chebyshev–Halley type methods with or without memory for solving nonlinear equations

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Cited by 15 publications
(28 citation statements)
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“…Due to change (5), the parameters in (4) does not remain as before and we denote them by n τ and n α  . We call the iterations ( 1) and ( 4) the derivative presence (DP) and derivative-free (DF) variants respectively.…”
Section: The Optimal Derivative-free Three-point Iterationsmentioning
confidence: 99%
See 3 more Smart Citations
“…Due to change (5), the parameters in (4) does not remain as before and we denote them by n τ and n α  . We call the iterations ( 1) and ( 4) the derivative presence (DP) and derivative-free (DF) variants respectively.…”
Section: The Optimal Derivative-free Three-point Iterationsmentioning
confidence: 99%
“…Theorem 3. The iteration (4) with n τ given by (7) and with n α  given by (11) have the order of convergence eight, if the following conditions hold:…”
Section: Application Of Sufficient Convergence Condition To Derive New Df Iterationsmentioning
confidence: 99%
See 2 more Smart Citations
“…Finally, we compare them with schemes proposed by Argyros et al [1], out of them we consider expression (2.4) with (H 1 (τ ), γ = −0.01, α = 1) and (H 2 (τ ), γ = −0.01, α = 0), called by AM 1 and AM 2 , respectively. Actually, the methods AM 1 and AM 2 are designed only for simple roots according to their paper.…”
Section: Numerical Illustrationsmentioning
confidence: 99%