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A graphical compensation approach for smoothing the one-dimensional canonical piecewise-linear model

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Abstract

In this paper, a new approach to smoothen the one-dimensional canonical piecewise-linear model is presented. Contrary to traditional smoothing strategies, the proposal preserves the algebraic form of the canonical representation and only adds terms (expressed by hyperbolic tangent and absolute value functions) that smoothly compensate the characteristic slope transitions in a piecewise-linear graph. In general terms, it is shown that the graph of any one-dimensional piecewise-linear function can be transformed into a smoother one by a graphical compensation at their knot points. Besides preserving the original form of the model, the proposal also allows controlling smoothness either globally (at all the breakpoints) or locally (by a different level at each breakpoint).

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Authors and Affiliations

  1. Facultad de Instrumentación Electrónica, Universidad Veracruzana, Xalapa, Veracruz, México

    V M Jimenez-Fernandez

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  1. V M Jimenez-Fernandez
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Correspondence to V M Jimenez-Fernandez.

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Jimenez-Fernandez, V.M. A graphical compensation approach for smoothing the one-dimensional canonical piecewise-linear model. Sādhanā 46, 175 (2021). https://doi.org/10.1007/s12046-021-01700-6

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  • DOI: https://doi.org/10.1007/s12046-021-01700-6

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