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

Nonlinear resistive networks, which can be characterized by the equation
f(x) =y
, where
f(\cdot)
is a continuous piecewise linear mapping of
R^{n}
into itself, are discussed.
x
is a point in
R^{n}
and represents a set of chosen network variables and
y
is an arbitrary point in
R^{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.