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The existence of local solutions can be obtained by utilizing the method of the standard regularization, and the regularities of the solutions can be derived by the argument similar to that in [18].
A standard regularization procedure is needed (see [8] for details).
It applies a hybrid approach based both on a standard regularization technique (like Tikhonov) and on Krylov filtering.
The second is a curvature dependent regularization (CDR), which aims at overcoming the tendency of standard regularization to shrink segmented areas.
Usually, the appropriate choice of the regularization parameter at each iteration in the standard regularization algorithm is a difficult issue in this kind of methods.
Furthermore, when both u and f are relatively smooth, some standard regularization techniques can be employed (see [11] for a more detailed overview).
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The standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations.
Afterwards, the standard Tikhonov regularization method is used to solve ill-conditional matrix equation, while the regularization parameter is chosen by the L-curve criterion.
A standard Tikhonov regularization method is applied to the approximation of this integral equation when the data is not exact.
The classifier parameters, θ, are estimated by minimizing the cross-entropy error with standard L2 regularization, as per Equation 1.
There is a significant improvement in performance as opposed to a conventional approach with standard L2 regularization, i.e. Figure 9.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com