An analog scheme for fixed-point computation-Part II: Applications

In a companion paper [see ibid., vol. 44, p. 351-4, 1997] we presented theoretical analysis of an analog network for fixed-point computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: (1) solving systems of linear equations; (2) nonlinear programming; (3) dynamic programing; and (4) network flow computations. Schematic circuits are proposed for representative cases and implementation issues are discussed. Exponential convergence is established for a fixed-point computation that determines the stationary probability vector for a Markov chain. A fixed-point formulation of the single source shortest path problem (SPP) that will always converge to the exact shortest path is described. A proposed implementation, on a 2-/spl mu/ complementary metal-oxide-semiconductor (CMOS) process, for a fully connected eight-node network is described in detail. The accuracy and settling time issues associated with the proposed design approach are presented.