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

Ioannis K. Argyros; Santhosh George

doi:10.33993/jnaat432-1025

Authors

Ioannis K. Argyros Cameron University, USA
Santhosh George National Institute of Technology Karnataka, India

DOI:

https://doi.org/10.33993/jnaat432-1025

Keywords:

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

Abstract views: 283

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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References

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