An Iterative Method for Curve Adjustment Based on Optimization of a Variable and its Application
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| Format: | Artículo científico |
| Language: | en |
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Universidad Nacional de Colombia
2014
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| _version_ | 1876439060286799872 |
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| author | Rogelio Acosta |
| author_facet | Rogelio Acosta |
| contents | An Iterative Method for Curve Adjustment Based on Optimization of a Variable and its Application Rogelio Acosta Suitberto Cabrera Luis Manuel Vega Asela Cabrera Nersa Acosta Física, Astronomía y Matemáticas Curve estimation Iterative method Linear regression Teaching materials Least Squares Method An iterative method for the adjustment of curves is obtained by applying the least squares method reiteratively in functional subclasses, each defined by one parameter, after assigning values to the rest of the parameters which determine a previously determined general functional class. To find the minimum of the sum of the squared deviations, in each subclass, only techniques of optimization are used for real functions of a real variable.The value of the parameter which gives the best approximation in an iteration is substituted in the general functional class, to retake the variable character of the following parameter and repeat the process, getting a succession of functions. In the case of simple linear regression, the convergence of that succession to the least squares line is demonstrated, because the values of the parameters that define each approximation coincide with the values of the parameters obtained when applying the method of Gauss - Seidel to the normal system of equations. This approach contributes to the teaching objective of improving the treatment of the essential ideas of curve adjustment, which is a very important topic in applications, what gives major importance to the optimization of variable functions. 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89931327008 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.1 Vol.37 |
| format | Artículo científico |
| id | redalyc_89931327008 |
| institution | Redalyc |
| language | en |
| publishDate | 2014 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | An Iterative Method for Curve Adjustment Based on Optimization of a Variable and its Application Rogelio Acosta Física, Astronomía y Matemáticas Curve estimation Iterative method Linear regression Teaching materials Least Squares Method An Iterative Method for Curve Adjustment Based on Optimization of a Variable and its Application Rogelio Acosta Suitberto Cabrera Luis Manuel Vega Asela Cabrera Nersa Acosta Física, Astronomía y Matemáticas Curve estimation Iterative method Linear regression Teaching materials Least Squares Method An iterative method for the adjustment of curves is obtained by applying the least squares method reiteratively in functional subclasses, each defined by one parameter, after assigning values to the rest of the parameters which determine a previously determined general functional class. To find the minimum of the sum of the squared deviations, in each subclass, only techniques of optimization are used for real functions of a real variable.The value of the parameter which gives the best approximation in an iteration is substituted in the general functional class, to retake the variable character of the following parameter and repeat the process, getting a succession of functions. In the case of simple linear regression, the convergence of that succession to the least squares line is demonstrated, because the values of the parameters that define each approximation coincide with the values of the parameters obtained when applying the method of Gauss - Seidel to the normal system of equations. This approach contributes to the teaching objective of improving the treatment of the essential ideas of curve adjustment, which is a very important topic in applications, what gives major importance to the optimization of variable functions. 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89931327008 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.1 Vol.37 |
| title | An Iterative Method for Curve Adjustment Based on Optimization of a Variable and its Application |
| topic | Física, Astronomía y Matemáticas Curve estimation Iterative method Linear regression Teaching materials Least Squares Method |
| url | https://www.redalyc.org/articulo.oa?id=89931327008 |