On a class of efficient higher order Newton-like methods
Abstract
Based on a two-step Newton-like scheme, we propose a three-step scheme of convergence order p+2 (p >=3) for solving systems of nonlinear equations. Furthermore, on the basis of this scheme a generalized k+2-step scheme with increasing convergence order p+2k is presented. Local convergence analysis including radius of convergence and uniqueness results of the methods is presented. Computational efficiency in the general form is discussed. Theoretical results are verified through numerical experimentation. Finally, the performance is demonstrated by the application of the methods on some nonlinear systems of equations.
Keywords:
Newton-like methods, convergence, Fr´echet-derivative, computational efficiencyHow to Cite
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Copyright (c) 2019 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2019 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.