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Inexact Newton Methods on Riemannian Manifolds

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Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI,volume 10)

Abstract

In this chapter we study of the Inexact Newton Method in order to solve problems on a Riemannian Manifold. We present standard notation and previous results on Riemannian manifolds. A local convergence study is presented and some special cases are also provided.

Keywords

  • Vector Field
  • Riemannian Manifold
  • Semilocal Convergence
  • Inexact Newton Method
  • Local Convergence Analysis

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

The research has been partially funded by UNIR Research (http://research.unir.net), Universidad Internacional de La Rioja (UNIR, http://www.unir.net), under the Research Support Strategy 3 [2015–2017], Research Group: MOdelación Matemática Aplicada a la INgeniería (MOMAIN), by the Grant SENECA 19374/PI/14 and by the project MTM2014-52016-C2-1-P of the Spanish Ministry of Economy and Competitiveness.

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Correspondence to Á. A. Magreñán .

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Argyros, I.K., Magreñán, Á.A. (2016). Inexact Newton Methods on Riemannian Manifolds. In: Amat, S., Busquier, S. (eds) Advances in Iterative Methods for Nonlinear Equations. SEMA SIMAI Springer Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-39228-8_4

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