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Isonormal surfaces: a new tool for the multidimensional dynamical analysis of iterative methods for solving nonlinear systems
  • Raudys Rafael Capdevila,
  • Alicia Cordero,
  • Juan Ramon Torregrosa
Raudys Rafael Capdevila
Universidad Politécnica de Valencia
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Alicia Cordero
Universidad Politécnica de Valencia
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Juan Ramon Torregrosa
Universidad Politécnica de Valencia
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Abstract

The dynamical behavior of the rational vectorial operator associated with a multidimensional iterative method in polynomial systems, gives us interesting information about the stability of the iterative scheme. The stability of fixed points, dynamic planes, bifurcation diagrams, etc. are known tools that act in this sense. In this manuscript, we introduce a new tool, which we call isonormal surface, to complement the information about the stability of the iterative method provided by the dynamic elements mentioned above. These dynamical instruments are used for analyze the stability of a parametric family of multidimensional iterative schemes in terms of the value of the parameter. Some numerical tests confirm the obtained dynamical results.

Peer review status:UNDER REVIEW

22 Oct 2020Submitted to Mathematical Methods in the Applied Sciences
23 Oct 2020Submission Checks Completed
23 Oct 2020Assigned to Editor
06 Dec 2020Reviewer(s) Assigned
16 May 2021Review(s) Completed, Editorial Evaluation Pending
24 May 2021Editorial Decision: Revise Minor
26 May 20211st Revision Received
26 May 2021Submission Checks Completed
26 May 2021Assigned to Editor
09 Jun 2021Reviewer(s) Assigned
10 Jun 2021Review(s) Completed, Editorial Evaluation Pending