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A theoretical proof of the system convergence is provided.
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As it can be seen in Tables 5 and 6 (respectively, Tables 7 and 8) where we reported the variations of E m m ′ (respectively, E m m ′ ν T ) as a function of the extraction degrees of the false components m and m ′, in the case of even even systems (respectively, odd systems), the convergence is also rapidly reached in the case of the energy (as soon as m = m ′ = 4 in all the considered cases).
For nonlinear systems, the convergence is not as tangible.
In the DROP program, the fitted ellipse has a strongly non-linear character (equation in the rotated co-ordinate system), and hence convergence is not rapid and depends strongly on the strategy employed.
In many cases, especially for systems, the iterative convergence is not sufficient to guaranty the theoretical accuracy.
In [6], a low-complexity adaptive algorithm is proposed for 2- or 4-state modulation systems but the convergence is rather slow, while in [7, 8] near minimum BER equalization is carried out by radial basis function neural networks which considerably increases the equalizer complexity.
An algorithm to approximate the initial state of a nonlinear system is described, and its convergence is also analyzed in detail.
This type of methods significantly reduces computational efforts for large systems; however, the uncertainty of convergence is a major concern.
One possible explanation for this convergence is that systems have learned from one another.
But the distinction between informatics products is blurring, says Markus Dathe, good manufacturing practice and computer system validation coordinator at Roche, because "convergence is happening".
Up to our knowledge, the iterative convergence is poor for systems, except for the blended scheme of Deconinck et al. [Á.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com