Section-wise piecewise-linear functions: Canonical representation, properties, and applications
- 1 June 1977
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 65 (6) , 915-929
- https://doi.org/10.1109/proc.1977.10589
Abstract
This paper presents a new closed form analytical formula for representing n-dimensional surfaces and scalar functions of n variables which are piecewise-linear over each cross section obtained by freezing any combination of n - 1 of the n coordinates. This new section-wise piecewise-linear representation can be easily programmed with efficient computer storage. It is a global representation in the sense that a single formula is used to compute for f(x1,x2,...,xn) for all values of (x1, x2,...., xn). Since this representation is expressed in closed analytic form, it allows standard mathematical operations and manipulations to be carried out in theorectical studies, In particular, it led to the possibility of deriving explicit closed form expressions for system parameters and design formulas. Examples are given which illustrate the potential applications of this representation in the modeling and analysis of nonlinear devices, circuits and systems.Keywords
This publication has 5 references indexed in Scilit:
- Solving piecewise‐linear equations for resistive networksInternational Journal of Circuit Theory and Applications, 1976
- Memristive devices and systemsProceedings of the IEEE, 1976
- An algorithm for modeling the sinusoidal input/steady-state response behavior of nonlinear systems over a set of frequencies and amplitudesJournal of the Franklin Institute, 1974
- Modeling of three terminal devices: A black box approachIEEE Transactions on Circuit Theory, 1972
- Piecewise-Linear Theory of Nonlinear NetworksSIAM Journal on Applied Mathematics, 1972