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Algorithms 2017, 10(1), 10; doi:10.3390/a10010010

Estimating the Local Radius of Convergence for Picard Iteration

Department of Informatics, West University of Timisoara, B-dul V. Parvan No. 4, 300223 Timisoara, Romania
Academic Editor: Henning Fernau
Received: 10 October 2016 / Revised: 28 December 2016 / Accepted: 30 December 2016 / Published: 9 January 2017
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Abstract

In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical to the best ones. As the algorithm does not require to evaluate the norm of derivatives, the computing effort is relatively low. View Full-Text
Keywords: fixed point; Picard iteration; local convergence; radius of convergence fixed point; Picard iteration; local convergence; radius of convergence
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Măruşter, Ş. Estimating the Local Radius of Convergence for Picard Iteration. Algorithms 2017, 10, 10.

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