High-level canonical piecewise linear representation using a simplicial partition

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