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Journal of Applied Mathematics and Computing

, Volume 25, Issue 1–2, pp 345–351 | Cite as

An improved unifying convergence analysis of Newton’s method in Riemannian manifolds

  • Ioannis K. Argyros
Article

Abstract

Using more precise majorizing sequences we provide a finer convergence analysis than before [1], [7] of Newton’s method in Riemannian manifolds with the following advantages: weaker hypotheses, finer error bounds on the distances involved and a more precise information on the location of the singularity of the vector field.

AMS Mathematics Subject Classification

65H10 65B05 65G99 47H17 49M15 

Key words and phrases

Newton’s method Riemannian manifold local/semilocal convergence singularity of a vector field Newton-Kantorovich method 

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References

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Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCameron UniversityLawtonUSA

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