A relationship between several piecewise-linear (PWL) techniques and continuation methods is established. Based on the given link, a systematic search method is derived from a continuation method for obtaining multiple solutions of PWL resistive networks. Depending on the nature of the Jacobian, the rules for a sign change in the algorithm are determined so that the root-finding procedure can be continued. Multiple solutions are obtained by tracing along a particular solution curve. Sufficient conditions for finding all multiple solutions are also provided.
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Lee et al. (1983) studied this question.
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