Smoothing the High Level Canonical Piecewise-Linear Model by an Exponential Approximation of its Basis-Function

Authors

  • Victor M. Jimenez-Fernandez Universidad Veracruzana
  • Maribel Jimenez-Fernandez Universidad Veracruzana
  • Hector Vazquez-Leal Universidad Veracruzana
  • Uriel A. Filobello-Nino Universidad Veracruzana
  • Francisco J. Castro-Gonzalez Universidad Veracruzana

DOI:

https://doi.org/10.13053/cys-20-2-2290

Keywords:

High-Level-Canonical, piecewise-linear, smoothing, basis-function, approximation.

Abstract

Piecewise-linear models constitute an attractive alternative to construct a function whose graph fits a finite set of discrete points. These models are preferably selected over other approximation strategies like polynomials or splines. Although there are several piecewise-linear models reported in literature, the so-called High Level Canonical has the remarkable advantage of emerging from a well-structured algorithmic methodology to efficiently determine the parameters of any given piecewise-linear function. However, as it happens in all other piecewise-linear models, it also has the problem of lack of differentiability at the breakpoints. In order to solve this problem, an approach based on an exponential approximation of the basis-function is proposed as a strategy to transform the High Level Canonical piecewise-linear model into a smooth-piecewise one. This mathematical transformation ensures the existence and continuity of the nth-order derivatives of the resulting smooth model. Besides of this, it is observed that by applying the piecewise-linear to smooth transformation, the number of terms of the resulting smooth representation can significantly be reduced due to a great number of them can be approximated by a line equation. In order to verify the effectiveness of this proposal, numerical simulations performed on one-dimensional and two-dimensional functions are reported.

Author Biographies

Victor M. Jimenez-Fernandez, Universidad Veracruzana

Victor Manuel Jimenez Fernandez received the B.Sc. degree in Electronic Engineering from the Technological Institute of Veracruz in 1998, the M.Sc. degree from the University of the Americas-Puebla (UDLA) in 2000, and the Ph.D. degree from the National Institute of Astrophysics, Optics, and Electronics (INAOE), Puebla, Mexico, in 2006, both in Electronic Sciences. Since 2009 he has been Professor at the School of Electronic Instrumentation of the University of Veracruz (UV),  Mexico. His main research interest is application of nonlinear models in engineering.

Maribel Jimenez-Fernandez, Universidad Veracruzana

Maribel Jimenez Fernandez received the B.Sc. degree in Pharmaceutical Chemistry and Biology from the University of Veracruz (UV) in 1997, the M.Sc. in Food Sciences from the University of the Americas-Puebla (UDLA) in 2000, and the Ph.D. degree in Food Biochemistry from the Technological Institute of Veracruz in 2006. She is currently with the Basic Sciences Institute (ICB) of the University of Veracruz. Her research interests include microencapsulation and microbiology in food technology.

Hector Vazquez-Leal, Universidad Veracruzana

Hector Vazquez-Leal received the B.Sc. degree in Electronic Instrumentation Engineering from the University of Veracruz (UV) in 1999, the M.Sc. and Ph.D. degrees in Electronic Sciences from the National Institute of Astrophysics, Optics, and Electronics (INAOE), Mexico, in 2001 and 2005, respectively. His current research mainly covers analytical-numerical solutions and symbolic analysis of nonlinear problems. Since 2010 he has been Professor at the School of Electronic Instrumentation of the University of Veracruz (UV), Mexico.

Uriel A. Filobello-Nino, Universidad Veracruzana

Uriel Antonio Filobello Niño received the B.Sc. degree in Physics from the University of Veracruz (UV) in 1991, the M.Sc. and Ph.D. degrees in Physics from the National Autonomous University of Mexico (UNAM), Mexico, in 2002 and 2007, respectively. He is currently Professor at the School of Electronic Instrumentation of the University of Veracruz, Mexico. His main research interest covers analytical-numerical methods for ordinary differential equations.

Francisco J. Castro-Gonzalez, Universidad Veracruzana

Francisco Javier Castro-Gonzalez received his B.Sc. in Communication and Electronic Engineering from the University of Xalapa, Veracruz, Mexico, in 2004, and the M.Sc. and Ph.D. from the National Institute of Astrophysics, Optics, and Electronics (INAOE), Puebla, Mexico, in 2009 and 2015, respectively. He currently works as a Postdoctoral Researcher at the University of Veracruz (UV). His research interests include device modeling and simulation of hybrid circuits (MOSFET-SETs) and computer-aided design and nonlinear circuit analysis.

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Published

2016-06-25

Issue

Vol. 20 No. 2 (2016): 20-2 (2016)

Section

Articles

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