An analog scheme for fixed point computation: I. Iheory

Abstract

An analog system for fixed point computation is described. The system is derived from a continuous time analog of the classical over-relaxed fixed point iteration. The dynamical system is proved to converge for nonexpansive mappings under all p norms, p∈(1,∞). This extends previously established results to not necessarily differentiable maps which are nonexpansive under the 8-norm. The system will always converge to a single fixed point in a connected set of fixed points. This allows the system to function as a complementary paradigm to energy minimization techniques for optimization in the analog domain. It is shown that the proposed technique is applicable to a large class of dynamic programming computations.