Tikhonov replacement functionals for iteratively solving nonlinear operator equations

@article{Ramlau2005TikhonovRF,
  title={Tikhonov replacement functionals for iteratively solving nonlinear operator equations},
  author={Ronny Ramlau and Gerd Teschke},
  journal={Inverse Problems},
  year={2005},
  volume={21},
  pages={1571 - 1592}
}
We shall be concerned with the construction of Tikhonov-based iteration schemes for solving nonlinear operator equations. In particular, we are interested in algorithms for the computation of a minimizer of the Tikhonov functional. To this end, we introduce a replacement functional, that has much better properties than the classical Tikhonov functional with nonlinear operator. Namely, the replacement functional is globally convex and can effectively be minimized by a fixed point iteration. On… 

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