EXPANDING THE APPLICABILITY OF A TWO STEP NEWTON LAVRENTIEV METHOD FOR ILL-POSED PROBLEMS

Authors

  • I. Argyros Department of Mathematicsal Sciences, Cameron University, Lawton, OK 73505, USA
  • S. George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-757 025

Abstract

In [3] we presented a cubically convergent Two Step Directional NewtonMethod (TSDNM) for approximating a solution of an operator equation in a Hilbert space setting. George and Pareth in [13] use the analogous Two Step Newton Lavrentiev Method (TSNLM) to approximate a solution of an ill-posed equation. In the present paper we show how to expand the applicability of (TSNLM). In particular, we present a semilocal convergence analysis of (TSNLM) under: weaker hypotheses, weaker convergence criteria, tighter error estimates on the distances involved and an at least as precise information on the location of the solution.

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Published

2013-07-07

How to Cite

Argyros, I., & George, S. (2013). EXPANDING THE APPLICABILITY OF A TWO STEP NEWTON LAVRENTIEV METHOD FOR ILL-POSED PROBLEMS. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 4(2), 1-15. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/242

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Section

Research Article

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