In this paper, a stable approximate solution of a nonlinear ill-posed operator equation of the form \(F(x)=y\) is obtained using simplified iteratively regularized Gauss-Newton method in Hilbert scales using Morozov type stopping rule. The advantage of using Hilbert scales is that it overcomes saturation effect of some of the regularization methods. We have obtained convergence rate results for the method under suitable non-linearity condition on the operator F.

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Simplified Iteratively Regularized Gauss-Newton Method in Hilbert Scales

  • Pallavi Mahale,
  • Ankush Kumar

摘要

In this paper, a stable approximate solution of a nonlinear ill-posed operator equation of the form \(F(x)=y\) is obtained using simplified iteratively regularized Gauss-Newton method in Hilbert scales using Morozov type stopping rule. The advantage of using Hilbert scales is that it overcomes saturation effect of some of the regularization methods. We have obtained convergence rate results for the method under suitable non-linearity condition on the operator F.