A sparse matrix method for analysis of piecewise-linear resistive networks

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Abstract
Nonlinear resistive networks, which can be characterized by the equationf(x) =y, wheref(\cdot)is a continuous piecewise linear mapping ofR^{n}into itself, are discussed.xis a point inR^{n}and represents a set of chosen network variables andyis an arbitrary point inR^{n}and represents the input to the network. New theorems on the existence of solutions together with a convergent method for obtaining at least one of the solutions are given. Also dealt with is an efficient computational algorithm which is especially suited for analysis of large piecewise-linear networks. The effectiveness of the method in terms of the amount of computation and data handling and storage is demonstrated.