Geodesic
Two-point methods for solving equations and systems of equations
Ioannis K. Argyros 1   ; Santhosh George 2
1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0003-1609-3195">ORCID: 0000-0003-1609-3195</a>
2 Department of Mathematical and Computational Sciences NIT Karnataka Karnataka, India 575 025 <a href="https://orcid.org/0000-0002-3530-5539">ORCID: 0000-0002-3530-5539</a>
Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 255-272 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The aim of this study is to present a convergence analysis of a frozen secant-type method for solving nonlinear systems of equations defined on the $k$-dimensional Euclidean space. The novelty of the paper lies in the fact that the method is defined using a special divided difference which is well defined for distinct iterates making it suitable for solving systems involving a nondifferentiable mapping. The local and semi-local convergence analysis is based on generalized Lipschitz-type scalar functions that are only nondecreasing, whereas their continuity is not assumed as in earlier studies. Numerical examples involving systems of equations are provided to further validate the theoretical results.
DOI : 10.4064/am2365-5-2018
Keywords: study present convergence analysis frozen secant type method solving nonlinear systems equations defined k dimensional euclidean space novelty paper lies the method defined using special divided difference which defined distinct iterates making suitable solving systems involving nondifferentiable mapping local semi local convergence analysis based generalized lipschitz type scalar functions only nondecreasing whereas their continuity assumed earlier studies numerical examples involving systems equations provided further validate theoretical results

Ioannis K. Argyros  1   ; Santhosh George  2

1 Department of Mathematical Sciences Cameron University Lawton, OK 73505, USA <a href="https://orcid.org/0000-0003-1609-3195">ORCID: 0000-0003-1609-3195</a>
2 Department of Mathematical and Computational Sciences NIT Karnataka Karnataka, India 575 025 <a href="https://orcid.org/0000-0002-3530-5539">ORCID: 0000-0002-3530-5539</a> 
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     title = {Two-point methods for solving equations and systems of equations},
     journal = {Applicationes Mathematicae},
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Ioannis K. Argyros; Santhosh George. Two-point methods for solving equations and systems of equations. Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 255-272. doi: 10.4064/am2365-5-2018

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