In this chapter, the local convergence behaviors of various blind equalization algo­ rithms are addressed. The local convergences of Godard algorithm (GA), ShalviWeinstein algorithm (SWA), and a standard-cumulant algorithm (SCA) are first demonstrated for linear FIR equalizers. A geometric relationship between the Go­ dard algorithm (or the equivalent constant modulus algorithm) and the SWA is revealed. In fact, both algorithms share the same local or global convergence char­ acteristics. The specific convergence points of the SWA equalizer are shown to be influenced by a kurtosis condition which can be exploited for initializing equalizer parameters.