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Similarly, for L=2, the mean convergence analysis could be performed for the corresponding algorithm in the family.
The complete mean convergence analysis for the generalized case with arbitrary value of L is quite involved.
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In this paper, we establish a nice convergence analysis by means of a novel integral operator approach.
Convergence analysis in the mean square sense is presented to prove the stability and steady-state performance.
Thus, our analysis provides the mean convergence bounds of the existing SSLMS algorithm which was not provided in the original work [7].
Then a convergence analysis is provided by means of the Chernoff bounds, which guarantees robustness in mean and in probability.
To this purpose, we have quantified by computer-assisted image analysis the profiles over 10 segments (mean convergence ≥7) crossing the plaques of each aortic cusp of each mouse (30 profiles/immunostain/mouse; Fig. 5A).
This means that Theorem 3.1 is a generalization of the convergence analysis of the Halpern algorithm.
The convergence analysis as well as the learning laws were produced by means of a Lyapunov Krasovskii functional.
Theorem 3.1 (Mean convergence).
Stochastic convergence analysis is provided.
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