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Open AccessFeature PaperArticle

Local Convergence of an Efficient Multipoint Iterative Method in Banach Space

1
Department of Mathematics, Sant Longowal Institute of Engineering & Technology, Punjab 148106, India
2
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(1), 25; https://doi.org/10.3390/a13010025
Received: 19 December 2019 / Revised: 11 January 2020 / Accepted: 13 January 2020 / Published: 15 January 2020
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. View Full-Text
Keywords: Banach space; divided difference; system of equations; order of convergence Banach space; divided difference; system of equations; order of convergence
MDPI and ACS Style

Sharma, J.R.; Kumar, S.; Argyros, I.K. Local Convergence of an Efficient Multipoint Iterative Method in Banach Space. Algorithms 2020, 13, 25.

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