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Evolutionary computation for optimal knots allocation in smoothing splines
Authors:Olga Valenzuela  Blanca Delgado-Marquez  Miguel Pasadas
Affiliation:1. Department of Applied Mathematics, University of Granada, Spain;2. Department of International and Spanish Economics, University of Granada, Spain
Abstract:In this paper, a novel methodology is presented for optimal placement and selections of knots, for approximating or fitting curves to data, using smoothing splines. It is well-known that the placement of the knots in smoothing spline approximation has an important and considerable effect on the behavior of the final approximation [1]. However, as pointed out in [2], although spline for approximation is well understood, the knot placement problem has not been dealt with adequately. In the specialized bibliography, several methodologies have been presented for selection and optimization of parameters within B-spline, using techniques based on selecting knots called dominant points, adaptive knots placement, by data selection process, optimal control over the knots, and recently, by using paradigms from computational intelligent, and Bayesian model for automatically determining knot placement in spline modeling. However, a common two-step knot selection strategy, frequently used in the bibliography, is an homogeneous distribution of the knots or equally spaced approach [3].
Keywords:Knots allocation   Approximation   Cubic spline
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