Chapter 3
Convergence and stability analysis
3.1 Introduction
In Chapter 2 we utilized averaging theory to gain insight into the stability and convergence performance of different partial-update techniques. While averaging theory allows significant simplification in the analysis of adaptive filters, its application is only limited to cases where the step-size parameter is very small. Stochastic gradient algorithms derived from an instantaneous approximation of the steepest descent algorithm and its variants behave differently to their averaged approximations as the step-size gets larger. This difference in convergence behaviour is attributed to gradient noise caused by removal of the expectation operator.
This chapter provides an in-depth ...
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