Sentence examples for discrepancy rule from inspiring English sources

Therefore, the Morozov discrepancy rule of Equation (22) is modified using the following theorem.

Consequently, a stopping criterion based on the Morozov discrepancy rule is investigated and tested.

Moreover, the Morozov discrepancy rule requires the noise level information and therefore cannot be used in many practical settings.

Moreover, the discrepancy error δ due to not satisfying the Morozov discrepancy rule is given by δ = ρ − e p o p t 2 (25).

They used the Morozov discrepancy rule to stop the LPIC iterations prior to final convergence in order to avoid noise magnification.

The difference between the norm of the residual error and the noise level is termed the discrepancy error δ and it quantifies the amount of discrepancy resulting from using the modified Morozov discrepancy rule of Equation (22) instead of the exact one described by Equation (21). Figure 8 Illustration of the Morozov discrepancy rule.

We propose to choose the regularization parameter by an a posteriori rule using the discrepancy principle.

Towards that objective, we investigate a stopping rule based on the Morozov discrepancy principle [17].

Using the Morozov discrepancy principle, we obtain an a posteriori parameter choice rule which only depends on the measured data.

Using the discrepancy principle, we provide a new a posteriori parameter choice rule.

There are many other examples, including in particular, the so-called low discrepancy quadrature rules, see, e.g., [13] for a detailed discussion and further references.