About this paper

Appears in:
Pages: 9384-9390
Publication year: 2017
ISBN: 978-84-617-8491-2
ISSN: 2340-1079
doi: 10.21125/inted.2017.2214

Conference name: 11th International Technology, Education and Development Conference
Dates: 6-8 March, 2017
Location: Valencia, Spain

A TEACHING APPLICATION FOR THE STUDY OF LEAST SQUARES APPROXIMATION USING CUBIC SPLINES

One of the most commonly used interpolation methods is based on the use of cubic splines due to their ease of handling (these are functions with a second continuous derivative and that, in pieces, are given by cubic polynomials) and its good geometric properties (they are the curves with the smallest "curvature" that happen through a given points). Splines can also be used to find the best least-squares approximation for a set of given points. In this paper we present a virtual laboratory of Matlab that allows to study graphically the least squares approximation through cubic splines and their properties. It is possible to work from a set of points of the given plane or from a curve defined by a function. In this case, in addition to the graphical representation of the given points, the exact curve and the least squares approximation, the graph of the error can also be obtained. The application can show the polynomial approximation by least squares allowing to compare both methods. Simplicity of handling, speed of calculation, interactivity and multiple graphical options can help students to better understand the concept of quadratic least approximation by splines, their properties and comparison with other methods.
@InProceedings{GIMENEZLUJAN2017ATE,
author = {Gim{\'{e}}nez Luj{\'{a}}n, J.F. and Fern{\'{a}}ndez de C{\'{o}}rdoba Castell{\'{a}}, P. and Gim{\'{e}}nez Palomares, F. and Monsoriu Serr{\'{a}}, J.A.},
title = {A TEACHING APPLICATION FOR THE STUDY OF LEAST SQUARES APPROXIMATION USING CUBIC SPLINES},
series = {11th International Technology, Education and Development Conference},
booktitle = {INTED2017 Proceedings},
isbn = {978-84-617-8491-2},
issn = {2340-1079},
doi = {10.21125/inted.2017.2214},
url = {http://dx.doi.org/10.21125/inted.2017.2214},
publisher = {IATED},
location = {Valencia, Spain},
month = {6-8 March, 2017},
year = {2017},
pages = {9384-9390}}
TY - CONF
AU - J.F. Giménez Luján AU - P. Fernández de Córdoba Castellá AU - F. Giménez Palomares AU - J.A. Monsoriu Serrá
TI - A TEACHING APPLICATION FOR THE STUDY OF LEAST SQUARES APPROXIMATION USING CUBIC SPLINES
SN - 978-84-617-8491-2/2340-1079
DO - 10.21125/inted.2017.2214
PY - 2017
Y1 - 6-8 March, 2017
CI - Valencia, Spain
JO - 11th International Technology, Education and Development Conference
JA - INTED2017 Proceedings
SP - 9384
EP - 9390
ER -
J.F. Giménez Luján, P. Fernández de Córdoba Castellá, F. Giménez Palomares, J.A. Monsoriu Serrá (2017) A TEACHING APPLICATION FOR THE STUDY OF LEAST SQUARES APPROXIMATION USING CUBIC SPLINES, INTED2017 Proceedings, pp. 9384-9390.
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