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http://dx.doi.org/10.4134/CKMS.c210306

ON THE SEMI-LOCAL CONVERGENCE OF CONTRAHARMONIC-MEAN NEWTON'S METHOD (CHMN)  

Argyros, Ioannis K. (Department of Mathematical Sciences Cameron University)
Singh, Manoj Kumar (Department of Mathematics Institute of Science Banaras Hindu University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 1009-1023 More about this Journal
Abstract
The main objective of this work is to investigate the study of the local and semi-local convergence of the contraharmonic-mean Newton's method (CHMN) for solving nonlinear equations in a Banach space. We have performed the semi-local convergence analysis by using generalized conditions. We examine the theoretical results by comparing the CHN method with the Newton's method and other third order methods by Weerakoon et al. using some test functions. The theoretical and numerical results are also supported by the basins of attraction for a selected test function.
Keywords
Banach space; Newton's method; semi-local convergence; order of convergence; efficiency index;
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