Abstract: The rate of convergence of an adaptive system is optimized as a function of the stability with which it converges to a desired state. In the adaptive technique according to the invention, for optimal convergence, a large adaptive coefficient value is used in stable regions with relatively smaller noise, while a smaller adaptive coefficient is used in unstable or noisy environments. Also when the solution has been reached &mgr; is decreased to decrease the effects of noise and the residual error. Various algorithms are used to evaluate the stability with which the system converges and to select a corresponding adaptive coefficient. The method and apparatus according to the invention provides an optimum rate of convergence based on the overall stability of the system, while minimizing the residual error.