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Canonical piecewise-linear representation

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2 Author(s)
Chua, L.O. ; Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA ; Deng, A.-C.

Every continuous piecewise-linear function of one variable f :R1R1 has a unique canonical piecewise-linear representation. However, only a subclass of higher-dimensional piecewise-linear functions f:RnRn, n>1, has a canonical piecewise-linear representation. It is proved that the necessary and sufficient conditions for the existence of a canonical piecewise-linear representation is that fpossess a consistent variation property. The geometrical constraints imposed by this property are analyzed and discussed in detail along with many examples

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Circuits and Systems, IEEE Transactions on  (Volume:35 ,  Issue: 1 )