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<p>We show that the Newton method applied to a system of nonlinear equations after transformation of its variables and the Newton method applied to a transformation of the equations themselves (nonlinear preconditioning) can be interpreted within the general perturbed Newtonian framework. This gives an insight into the nature of those methods from a unified perspective, as well as some new convergence results in the case when solutions are singular.</p>

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Transformations of variables and transformations of equations via the perturbed Newton method framework

  • 期刊论文

  • 发表日期：

    2025年11月10日

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  • Alexey F. Izmailov,
  • Mikhail V. Solodov

摘要

We show that the Newton method applied to a system of nonlinear equations after transformation of its variables and the Newton method applied to a transformation of the equations themselves (nonlinear preconditioning) can be interpreted within the general perturbed Newtonian framework. This gives an insight into the nature of those methods from a unified perspective, as well as some new convergence results in the case when solutions are singular.