On the Local Convergence of a Sixth-Order Iterative Scheme in Banach Spaces

Parhi, Sanjaya Kumar; Sharma, Debasis

doi:10.1007/978-981-16-1402-6_7

Cited by 1 publication

(3 citation statements)

References 23 publications

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“…We observe that, ρ = ρ in the above examples. Furthermore, note that we can obtain a better radius of convergence than that of Parhi and Sharma's convergence analysis in [9].…”

Section: Estimation Of Radius Of Convergence and Computational Ordermentioning

confidence: 70%

“…Then, , ρ 1 , ρ2 } ≈ 0.4510. Parhi and Sharma [9] considered this example 2 and obtained the radius R = 0.133649. Remark 2.…”

Section: Estimation Of Radius Of Convergence and Computational Ordermentioning

confidence: 99%

“…In [9], Parhi and Sharma proved the convergence of the method (4) without using Taylor expansion. However, the authors could not obtain the sixth-order convergence theoretically for method (4).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extending the Applicability of Cordero Type Iterative Method

Remesh

Argyros

et al. 2022

Symmetry

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Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero’s method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting.

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“…We observe that, ρ = ρ in the above examples. Furthermore, note that we can obtain a better radius of convergence than that of Parhi and Sharma's convergence analysis in [9].…”

Section: Estimation Of Radius Of Convergence and Computational Ordermentioning

confidence: 70%

“…Then, , ρ 1 , ρ2 } ≈ 0.4510. Parhi and Sharma [9] considered this example 2 and obtained the radius R = 0.133649. Remark 2.…”

Section: Estimation Of Radius Of Convergence and Computational Ordermentioning

confidence: 99%