Title :
A compact f-f model of high-dimensional piecewise-linear function over a degenerate intersection
Author :
Wen, Chengtao ; Wang, Shuning ; Li, Feng ; Khan, M.J.
Author_Institution :
Dept. of Autom., Tsinghua Univ., Beijing, China
fDate :
4/1/2005 12:00:00 AM
Abstract :
A novel f-f model is developed constructively which can express any n-dimensional piecewise linear (PWL) function by a superposition of basis functions if it is defined over an nth-order degenerate intersection formed by (n-1)th-order minimal degenerate intersections. We also propose the concrete functional forms of nth-order basis functions. Being the simplest type of the minimal degenerate intersection, the basis function is the most elementary "building block" of a PWL function defined in an arbitrary-dimensional space. In addition, the model constitutes a natural continuation to Julian\´s canonical formulation and can bridge the lattice PWL model and the well-established canonical representation.
Keywords :
function approximation; network analysis; piecewise linear techniques; arbitrary-dimensional space; canonical formulation; compact f-f model; cutting algorithm; degenerate intersection; lattice PWL model; nth-order basis functions; piecewise-linear function; Bridge circuits; Circuit analysis; Concrete; Function approximation; Helium; Lattices; Modeling; Piecewise linear techniques; Systems engineering and theory; Two dimensional displays; Basis function; cutting algorithm; lattice PWL model; piecewise-linear (PWL) representation;
Journal_Title :
Circuits and Systems I: Regular Papers, IEEE Transactions on
DOI :
10.1109/TCSI.2005.844367