Expanding the applicability of Newton-Tikhonov method for ill-posed equations

Authors

  • Ioannis K. Argyros Cameron University
  • Santhosh George National Institute of Technology Karnataka

Keywords:

Newton-Tikhonov method, Hilbert space, semilocal convergence, majorizing sequence, Hammerstein operator, ill-posed problem

Abstract

We present a new semilocal convergence analysis of Newton- Tikhonov methods for solving ill-posed operator equations in a Hilbert space setting. Using more precise majorizing sequences and under the same computational cost as in earlier studies such as [13]-[20], we provide: weaker sufficient convergence criteria; tighter error estimates on the distances involved and an at least as precise information on the location of the solution. Applications include Hammertein nonlinear integral equations.

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Published

2014-08-01

How to Cite

Argyros, I. K., & George, S. (2014). Expanding the applicability of Newton-Tikhonov method for ill-posed equations. Rev. Anal. Numér. ThéOr. Approx., 43(2), 141-158. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2014-vol43-no2-art4

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