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Almost-sure convergence of adaptive algorithms by projections

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2 Author(s)
Voltz, P. ; Polytech. Univ., Farmingdale, NY, USA ; Kozin, F.

A convergence proof is discussed for the normalized least-mean-square (LMS) algorithm for ergodic inputs. The approach is based on interpreting the algorithm as a sequence of relaxed projection operators by which the key contraction property is derived. The proof technique is strongly motivated by physical intuition, and provides additional insight into LMS-type algorithms under ergodic inputs. Embedded in the development is a slight generalization to a random time-varying gain parameter. This allows the incorporation of variations such as the LMS and signed LMS algorithms.<>

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Automatic Control, IEEE Transactions on  (Volume:34 ,  Issue: 3 )