Almost-sure convergence of adaptive algorithms by projections

Peter Voltz, F. Kozin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)325-327
Number of pages3
JournalIEEE Transactions on Automatic Control
Volume34
Issue number3
DOIs
StatePublished - Mar 1989

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Adaptive algorithms
Mathematical operators

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Almost-sure convergence of adaptive algorithms by projections. / Voltz, Peter; Kozin, F.

In: IEEE Transactions on Automatic Control, Vol. 34, No. 3, 03.1989, p. 325-327.

Research output: Contribution to journalArticle

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