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Finding all solutions of piecewise linear functions and application to circuit design
Author(s) -
Leenaerts D. M. W.,
Hegt J. A.
Publication year - 1991
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490190202
Subject(s) - underdetermined system , piecewise linear function , trace (psycholinguistics) , dimension (graph theory) , solution set , mathematics , set (abstract data type) , linear equation , hierarchy , disjunct , piecewise , space (punctuation) , linear space , algorithm , mathematical optimization , computer science , discrete mathematics , pure mathematics , mathematical analysis , population , philosophy , linguistics , demography , sociology , economics , market economy , programming language , operating system
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.