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Using decomposition of the nonlinear operator for solving non-differentiable problems
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  • Eva G. Villalba,
  • Miguel Hernandez,
  • Jose Hueso,
  • Eulalia Martínez
Eva G. Villalba
Instituto Universitario de Matemática Multidisciplinar Universitat Politècnica de València València Spain

Corresponding Author:[email protected]

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Miguel Hernandez
Dept of Mathematics and Computation University of La Rioja Logroño Spain
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Jose Hueso
Instituto Universitario de Matemática Multidisciplinar Universitat Politècnica de València València Spain
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Eulalia Martínez
Instituto Universitario de Matemática Multidisciplinar Universitat Politècnica de València València Spain
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Abstract

From decomposition method for operators, we consider Newton-like iterative processes for approximating solutions of nonlinear operators in Banach spaces. These iterative processes maintain the quadratic convergence of Newton's method. Since the operator decomposition method has its highest degree of application in non-differentiable situations, we construct Newton-type methods using symmetric divided differences, which allow us to improve the accessibility of the methods. Experimentally, by studying the basins of attraction of these methods, observe an improvement in the accessibility of derivative-free iterative processes that are normally used in these non-differentiable situations, such as the classic Steffensen's method. In addition, we study both the local and semi-local convergence of the Newton-type methods considered.
23 Sep 2022Submitted to Mathematical Methods in the Applied Sciences
23 Sep 2022Submission Checks Completed
23 Sep 2022Assigned to Editor
09 Oct 2022Reviewer(s) Assigned
14 Oct 2022Review(s) Completed, Editorial Evaluation Pending
04 Mar 2023Editorial Decision: Revise Major
13 Mar 20231st Revision Received
22 Mar 2023Submission Checks Completed
22 Mar 2023Assigned to Editor
22 Mar 2023Review(s) Completed, Editorial Evaluation Pending
24 Mar 2023Reviewer(s) Assigned
22 May 2023Editorial Decision: Accept