International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Newton's Method for Convex Operators and Applications

  • Octav Olteanu1
  1. "University Politehnica of Bucharest"

Abstract

This review work presents the general statement of a variant of Newton's method for convex monotone operators and its applications. We consider the estimation of the absolute error too. One makes the connection to the contraction principle. One of the applications is approximating where a positive selfadjoint operator is acting on a Hilbert space. One works with “global” convex monotone operators. For the local approach, we mention appropriate references.

How to Cite

O. Olteanu, Newton's Method for Convex Operators and Applications, Int. J. Anal. Appl. 4 (2014), 11–20.

BibTeX
@article{Olteanu2014,
  author  = {Olteanu, Octav},
  title   = {Newton's Method for Convex Operators and Applications},
  journal = {Int. J. Anal. Appl.},
  volume  = {4},
  year    = {2014},
  pages   = {11--20},
  doi     = {}
}

References

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  • [5] J. M., Olteanu, A. & Olteanu, O., Applications of Newton convex monotone operators, Mathematical Reports, 7(57), 3 (2005), 219-231.
  • [6] Olteanu, O. & Simion, Gh., A new geometric aspect of the implicit function principle and method for operators. Mathematical Reports 5 (55), 1 (2003), 61-84.