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High-level canonical piecewise linear representation using a simplicial partition

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3 Author(s)
Julian, P. ; Dept. de Ingenieria Electr., Univ. Nacional del Sur, Bahia Blanca, Argentina ; Desages, A. ; Agamennoni, O.

In this work, we propose a set of high-level canonical piecewise linear (HL-CPWL) functions to form a representation basis for the set of piecewise linear functions f: D→R1 defined over a simplicial partition of a rectangular compact set D in Rn. In consequence, the representation proposed uses the minimum number of parameters. The basis functions are obtained recursively by multiple compositions of a unique generating function γ, resulting in several types of nested absolute-value functions. It is shown that the representation in a domain in Rn requires functions up to nesting level n. As a consequence of the choice of the basis functions, an efficient numerical method for the resolution of the parameters of the high-level (HL) canonical representation results. Finally, an application to the approximation of continuous functions is shown

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:46 ,  Issue: 4 )