文章基本信息

标题：Smoothing the High Level Canonical Piecewise-Linear Model by an Exponential Approximation of its Basis-Function
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作者：Victor M. Jimenez-Fernandez ; Maribel Jimenez-Fernandez ; Hector Vazquez-Leal 等
期刊名称：Computación y Sistemas
印刷版ISSN：1405-5546
出版年度：2016
卷号：20
期号：2
页码：227-237
语种：English
出版社：Instituto Politécnico Nacional
其他摘要：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.
其他关键词：High-Level-Canonical; piecewise-linear; smoothing; basis-function; approximation.