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Acknowledgement to Reviewers of Computation in 2019
Article

Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions

1
Department of Mathematics, Cameron University, Lawton, OK 73505, USA
2
Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
*
Author to whom correspondence should be addressed.
Computation 2020, 8(1), 8; https://doi.org/10.3390/computation8010008
Received: 8 January 2020 / Revised: 20 January 2020 / Accepted: 23 January 2020 / Published: 26 January 2020
The technique of using the restricted convergence region is applied to study a semilocal convergence of the Newton–Kurchatov method. The analysis is provided under weak conditions for the derivatives and the first order divided differences. Consequently, weaker sufficient convergence criteria and more accurate error estimates are retrieved. A special case of weak conditions is also considered. View Full-Text
Keywords: Newton–Kurchatov method; ω-type conditions; ε-type conditions; method with decomposition of operator; semilocal convergence; divided differences; restricted convergence region Newton–Kurchatov method; ω-type conditions; ε-type conditions; method with decomposition of operator; semilocal convergence; divided differences; restricted convergence region
MDPI and ACS Style

Argyros, I.K.; Shakhno, S.; Yarmola, H. Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions. Computation 2020, 8, 8. https://doi.org/10.3390/computation8010008

AMA Style

Argyros IK, Shakhno S, Yarmola H. Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions. Computation. 2020; 8(1):8. https://doi.org/10.3390/computation8010008

Chicago/Turabian Style

Argyros, Ioannis K., Stepan Shakhno, and Halyna Yarmola. 2020. "Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions" Computation 8, no. 1: 8. https://doi.org/10.3390/computation8010008

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