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The final model was obtained after six iterations, by which point sufficient convergence was obtained with the rms misfit converging to better than 0.01 nT and the Euclidean norm of the model change in the final iteration less than 0.005 % that of the model itself.

We measured the number of iterations required for the GDA to converge, and we discarded runs in which no convergence was obtained after 10,000 steps.

Then, problems reduce to the generalized variational inequalities with perturbed operators considered in [10, Proposition 3.1] and the convergence was obtained under the assumption that the operators converge graphically.

In cases where the Hill model did not converge, the high-dose group was iteratively dropped until convergence was obtained.

In addition, the weak convergence was obtained on condition that the iteration sequence is bounded.

Results of the analytical mathematical model and the experiments were compared, good convergence was obtained.

Excellent convergence is obtained using these parameters, and the total energy is converged to 2.0 × 10−5 eV/atom.

Good convergence is obtained with these parameters and the total energy is converged to 2.0 × 10−5 eV/atom.

Then converges strongly to the unique fixed point, and the estimation of degree of convergence is obtained as follow: (2.19).

Good convergence is obtained with these parameters.

In particular, a stop criterion of convergence is obtained.