A Geometric Model Defined By A Family Of Splines For Modelling Complex Systems
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Y. Villacampa, F. G. Navarro-González, P. Cerdán & M. Cortés
The study of natural systems implies considering new modelling methodologies that are able to produce different relationships to those described with mathematical functions, which are derived from the geometry of Euclid. In this paper, the authors propose a geometric model defined by families of cubic Splines, which are the basis for a definition of a numerical methodology for the study and modelling of complex systems. Geometric models are applied in specific cases for types of relationships. One feature of the model is that the polynomials are not represented by their coefficients, because they could be highly dependent of small variations in their values, as it is analyzed in the article. The polynomials will be represented by their values at points considered in their ranges of definition, which will be called nodes. For each variable, a Spline generated from kl cubic polynomials is defined, so the first objective is the analysis of a family of Splines determined by a set of polynomials. Finally, the geometric model is determined on practical examples from experimental data and the advantages of using the new methodology, based on the identification of Splines by their values in a number of points, are discussed, compared with the usual definition from the polynomial coefficients. Keywords: modelling, complex systems, Splines.
Keywords: modelling, complex systems, Splines.