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Combined Newton‐Kurchatov method for solving nonlinear operator equations
Author(s) -
Iakymchuk Roman,
Shakhno Stepan,
Yarmola Halyna
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610348
Subject(s) - uniqueness , lipschitz continuity , nonlinear system , newton's method , mathematics , local convergence , convergence (economics) , operator (biology) , ball (mathematics) , mathematical analysis , iterative method , physics , mathematical optimization , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , economics , gene , economic growth
We investigate local and semi‐local convergence of the combined Newton‐Kurchatov method under the classical and generalized Lipschitz conditions for solving nonlinear equations. The convergence order of the method is examined and the uniqueness ball for the solution of the nonlinear equation is proved. Numerical experiments are conducted on test problems. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)