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On almost sure convergence of adaptive algorithms

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2 Author(s)
Shi, D. ; Xiamen University, China ; Kozin, F.

We present an extension of the Furstenberg-Kesten theorem on the convergence of random matrices. This extension is applied to the study of almost sure convergence of certain adaptive algorithms. In particular, we establish that the NLMS algorithm is almost surely convergent under extremely weak necessary and sufficient conditions. We also discuss the relationship of sufficient conditions that have appeared in the literature with our results.

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Automatic Control, IEEE Transactions on  (Volume:31 ,  Issue: 5 )