High Level Canonical Piecewise Linear Representation Using a Simplicial Partition

P. JULIÁN, A. DESAGES, O. AGAMENNONI

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS

IEEE

Lugar: NY; Año: 1999 vol. 46 p. 463 - 480

1057-7122

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 gamma , 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.