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Convergence analysis of weighted-Newton methods of optimal eighth order in Banach spaces

Publication Type : Journal Article

Publisher : Mathematics

Source : Mathematics. 7. 198. 10.3390/math7020198.

Url : https://www.researchgate.net/publication/331225826_Convergence_Analysis_of_Weighted-Newton_Methods_of_Optimal_Eighth_Order_in_Banach_Spaces

Campus : Chennai

School : School of Engineering

Department : Mathematics

Year : 2019

Abstract : We generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study their local convergence. In a previous study, the Taylor expansion of higher order derivatives is employed which may not exist or may be very expensive to compute. However, the hypotheses of the present study are based on the first Fréchet-derivative only, thereby the application of methods is expanded. New analysis also provides the radius of convergence, error bounds and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches that use Taylor expansions of derivatives of higher order. Moreover, the order of convergence for the methods is verified by using computational order of convergence or approximate computational order of convergence without using higher order derivatives. Numerical examples are provided to verify the theoretical results and to show the good convergence behavior.

Cite this Research Publication : Sharma, Janak & Argyros, Ioannis & Kumar, Sunil. (2019). Convergence Analysis of Weighted-Newton Methods of Optimal Eighth Order in Banach Spaces. Mathematics. 7. 198. 10.3390/math7020198.

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