Title :
High-level canonical piecewise linear representation using a simplicial partition
Author :
Julián, Pedro ; Desages, Alfredo ; Agamennoni, Osvaldo
Author_Institution :
Dept. de Ingenieria Electr., Univ. Nacional del Sur, Bahia Blanca, Argentina
fDate :
4/1/1999 12:00:00 AM
Abstract :
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
Keywords :
network parameters; nonlinear network analysis; piecewise linear techniques; basis functions; continuous functions; high-level canonical piecewise linear representation; multiple compositions; nested absolute-value functions; piecewise linear functions; rectangular compact set; representation basis; simplicial partition; Availability; Circuits; Nonlinear equations; Nonlinear systems; Piecewise linear approximation; Piecewise linear techniques; Power system modeling;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on