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→R{sup}1 defined over a simplicial partition of a rectangular compact set Din R{sup}n. In consequence, the representation proposed uses the minimum number of parameters. The basis functions are obtained recursively by multiple compositions of a unique generating functionγ, resulting in several types of nested absolute-valuefunctions. It is shown that the representation in a domain in R{sup}n 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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