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Traub-type high order iterative procedures on Riemannian manifolds

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Abstract

We present semilocal convergence results for Traub-type high convergence order iterative procedures for approximating zeros of a vector field on Riemannian manifolds. A characterization of the convergence under Kantorovich-type conditions and error estimates are also given in this study.

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Authors and Affiliations

  1. Dpto. de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, Spain

    S. Amat & S. Busquier

  2. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    I. K. Argyros

  3. Departamento de Matemáticas, facultad de Ciencias, Universidad de Valparaiso, Valparaiso, Chile

    R. Castro

  4. Dpto. de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Santiago, Chile

    S. Plaza

  5. Laboratoire de Mathématiques et Applications, Poitiers University, 86962 , Futuroscope Chasseneuil Cedex, France

    S. Hilout

Authors
  1. S. Amat
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  2. I. K. Argyros
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  3. S. Busquier
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  4. R. Castro
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  5. S. Hilout
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  6. S. Plaza
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Corresponding author

Correspondence to S. Amat.

Additional information

This paper is dedicated to the memory of Sergio Plaza.

Research of R. Castro and S. Plaza was supported by Fondecyt 10950252 (Chile).

Research of S. Amat and S. Busquier was supported by MICINN-FEDER MTM2010-17508 (Spain) and by 08662/PI/08 (Murcia).

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Amat, S., Argyros, I.K., Busquier, S. et al. Traub-type high order iterative procedures on Riemannian manifolds. SeMA 63, 27–52 (2014). https://doi.org/10.1007/s40324-014-0010-0

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