Finding all solutions of piecewise linear functions and applications to circuit design

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6 Citations (Scopus)


An algorithm is given for solving a set of underdetermined non-linear functions where some or all unknown variables are confined within a certain interval. the functions must be described by piecewise linear models with virtually no restriction to the dimension of the functions or models. the algorithm is able to find all separate solution points of equations on well-posed functions and can trace solution spaces, eventually composed of several disjunct branches, without any need for initial points. the presented methodology guarantees to find all solutions within a finite number of steps. In top-down circuit design, at each level one must solve a set of underdetermined equations in such a way that the solution space, if non-empty, is in agreement with solutions found earlier in the hierarchy. the presented algorithm can be used in such a hierarchical environment and guarantees to find all solutions at each level which are not in conflict with solutions found at higher levels.
Original languageEnglish
Pages (from-to)107-123
Number of pages17
JournalInternational Journal of Circuit Theory and Applications
Issue number2
Publication statusPublished - 1991


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