Smoothing the High Level Canonical Piecewise-Linear Model by an Exponential Approximation of its Basis-Function
| Autor: | Hector Vazquez-Leal, Maribel Jiménez-Fernández, F. Castro-Gonzalez, Uriel Filobello-Nino, Victor Manuel Jimenez-Fernandez |
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| Rok vydání: | 2016 |
| Předmět: |
General Computer Science
010401 analytical chemistry Mathematical analysis 020206 networking & telecommunications Basis function 02 engineering and technology Function (mathematics) 01 natural sciences 0104 chemical sciences Exponential function Piecewise linear function Transformation (function) 0202 electrical engineering electronic engineering information engineering Differentiable function Linear equation Smoothing Mathematics |
| Zdroj: | Computación y Sistemas. 20 |
| ISSN: | 2007-9737 1405-5546 |
| DOI: | 10.13053/cys-20-2-2290 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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