An Adaptive Curvature-Guided Approach for the Knot-Placement Problem in Fitted SplinesSource: Journal of Computing and Information Science in Engineering:;2018:;volume( 018 ):;issue: 004::page 41013Author:Aguilar, Enrique
,
Elizalde, Hugo
,
Cárdenas, Diego
,
Probst, Oliver
,
Marzocca, Pier
,
Ramirez-Mendoza, Ricardo A.
DOI: 10.1115/1.4040981Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper presents an adaptive and computationally efficient curvature-guided algorithm for localizing optimum knot locations in fitted splines based on the local minimization of an objective error function. Curvature information is used to narrow the searching area down to a data subset where the local error function becomes one-dimensional, convex, and bounded, thus guaranteeing a fast numerical solution. Unlike standard curvature-guided methods, typically relying on heuristic rules, the novel method here presented is based on a phenomenological approach as the error function to be minimized represents geometrical properties of the curve to be fitted, consequently reducing case-sensitivity issues and the possibility of defining spurious knots. A knot-readjustment procedure performed in the vicinity of a newly created knot has the ability of dispersing knots from otherwise highly knot-populated regions, a feature known to generate undesired local oscillations. The performance of the introduced method is tested against three other methods described in the literature, each handling the knot-placement problem via a different paradigm. The quality of the fitted splines for several datasets is compared in terms of the overall accuracy, the number of knots, and the computing efficiency. It is demonstrated that the novel algorithm leads to a significantly smaller knot vector and a much lower computing time, while preserving or improving the overall accuracy.
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contributor author | Aguilar, Enrique | |
contributor author | Elizalde, Hugo | |
contributor author | Cárdenas, Diego | |
contributor author | Probst, Oliver | |
contributor author | Marzocca, Pier | |
contributor author | Ramirez-Mendoza, Ricardo A. | |
date accessioned | 2019-02-28T11:12:17Z | |
date available | 2019-02-28T11:12:17Z | |
date copyright | 9/5/2018 12:00:00 AM | |
date issued | 2018 | |
identifier issn | 1530-9827 | |
identifier other | jcise_018_04_041013.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4253796 | |
description abstract | This paper presents an adaptive and computationally efficient curvature-guided algorithm for localizing optimum knot locations in fitted splines based on the local minimization of an objective error function. Curvature information is used to narrow the searching area down to a data subset where the local error function becomes one-dimensional, convex, and bounded, thus guaranteeing a fast numerical solution. Unlike standard curvature-guided methods, typically relying on heuristic rules, the novel method here presented is based on a phenomenological approach as the error function to be minimized represents geometrical properties of the curve to be fitted, consequently reducing case-sensitivity issues and the possibility of defining spurious knots. A knot-readjustment procedure performed in the vicinity of a newly created knot has the ability of dispersing knots from otherwise highly knot-populated regions, a feature known to generate undesired local oscillations. The performance of the introduced method is tested against three other methods described in the literature, each handling the knot-placement problem via a different paradigm. The quality of the fitted splines for several datasets is compared in terms of the overall accuracy, the number of knots, and the computing efficiency. It is demonstrated that the novel algorithm leads to a significantly smaller knot vector and a much lower computing time, while preserving or improving the overall accuracy. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | An Adaptive Curvature-Guided Approach for the Knot-Placement Problem in Fitted Splines | |
type | Journal Paper | |
journal volume | 18 | |
journal issue | 4 | |
journal title | Journal of Computing and Information Science in Engineering | |
identifier doi | 10.1115/1.4040981 | |
journal fristpage | 41013 | |
journal lastpage | 041013-9 | |
tree | Journal of Computing and Information Science in Engineering:;2018:;volume( 018 ):;issue: 004 | |
contenttype | Fulltext |