The classical Picard Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process.
Chung et al. [1] proposed a successive thresholding scheme for detecting shadows in color aerial images.
As has been mentioned, the successive cancelation scheme, as a simplified implementation of a BP concept, is used to decode PC.
Note that the BS is assumed to independently decode different users, i.e., it is not using a successive cancelation scheme at the receiver.
It should be noted that, when adopting the original BP technique, the error-correcting performance of PC can be further improved, compared with the currently simplified successive cancelation scheme.
Following [1], we now describe the original, unmodified, periodic successive approximations scheme for the p-periodic problem (3.2), (3.3) which we are going to modify and which is constructed as follows.
Indeed, it follows immediately from Corollary 6.7 that the periodic successive approximation scheme constructed with k interval halvings is applicable provided that r ( K ) < 2 k T ϱ ∗ (13.1).
Furthermore, the modest increase in AUC values with ever greater data partitioning would suggest that each successive partitioning scheme produced, at best, only slightly better fitting models.
The successive smoothing scheme described above is similar to a Laplacian pyramid [ 21], but we apply the Gaussian filters in the frequency domain with no downsampling.
As for the algorithm itself, we follow the approach of the DelPhi PBE solver, which exploits the checkerboard structure of the finite difference discretization of the Laplace differential operator and adopts a successive overrelaxation scheme to converge to the solution.
Close adherence to the biosynthetic hypothesis enabled us to identify a collection of natural products of progressively increasing complexity each of which could be used as a platform for the development of novel solutions to successive challenges (Scheme 1).
