Least squares data fitting

Least squares data fitting

 It is desired to represent, as good as possible, a series of data by means of certain functions with free parameters. "As good as possible" means that these parameters ara chosen so that the residuals, the difference between data and fitting functions, be as small as it is feasib...

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Autor Principal: Ripa, P
Formato: Online
Idioma:eng
Publicado: Iniversidad Autónoma de Baja California 2002
Acceso en liña:https://www.cienciasmarinas.com.mx/index.php/cmarinas/article/view/204
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spelling oai:cienciasmarinas.com.mx:article-2042019-05-02T21:27:17Z Least squares data fitting Ajuste de datos por cuadrados mínimos Ripa, P Least squares data fitting Mínimos cuadrados ajuste de datos  It is desired to represent, as good as possible, a series of data by means of certain functions with free parameters. "As good as possible" means that these parameters ara chosen so that the residuals, the difference between data and fitting functions, be as small as it is feasible. Our objective is not limited to finding the parameters of the best fit, but we also wish to know something about their uncertainties, this is, how well they are determined, given the errors of the original data as well as the imperfection of the fitting. Finally, supposing that we use the parameters of the fit in the calculation of other variables, we also want to have an estimation of the uncertainties of the latter. In order to do that, we imagine basic properties, wich we call "hypothesis", and then proceed from there with mathematical rigor. It is not superfluous to remember that the conclusions at wich we arrive depende on the hyphotheses done throughout the way, including the idea that useful information can be extracted from a least squares fit, of those data by these functions. Se desea representar, lo mejor posible, una serie de datos por medio de ciertas funciones con parámetros libres. "Lo mejor posible" significa que estos parámetros se eligen de manera que los residuos –la diferencia entre los datos y las funciones que se les ajustan– sean tan pequeños como se pueda. Nuestro objetivo no se limita a encontrar los parámetros del mejor ajuste, sino que también deseamos saber algo sobre sus incertidumbres, esto es, qué tan bien están determinados, dados tanto los errores de los datos originales como la imperfección del ajuste. Finalmente, suponiendo que utilizamos los parámetros del ajuste en el cálculo de otras variables, queremos también tener una estimación de las incertidumbres de estas últimas. Para poder avanzar, imaginamos propiedades básicas a las que llamamos "hipótesis", y de ahí procedemos con rigor matemático. No es malo tener presente que las conclusiones a las que lleguemos dependen de las hipótesis hechas a lo largo del camino –incluyendo la idea de que del ajuste por cuadrados mínimos de esos datos, por estas funciones, se pueda extraer una información útil. Iniversidad Autónoma de Baja California 2002-03-06 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Peer-reviewed Article Artículo Arbitrado application/pdf https://www.cienciasmarinas.com.mx/index.php/cmarinas/article/view/204 10.7773/cm.v28i1.204 Ciencias Marinas; Vol. 28 No. 1 (2002); 79-105 Ciencias Marinas; Vol. 28 Núm. 1 (2002); 79-105 2395-9053 0185-3880 eng https://www.cienciasmarinas.com.mx/index.php/cmarinas/article/view/204/171
institution Ciencias Marinas
collection OJS
language eng
format Online
author Ripa, P
spellingShingle Ripa, P
Least squares data fitting
author_facet Ripa, P
author_sort Ripa, P
title Least squares data fitting
title_short Least squares data fitting
title_full Least squares data fitting
title_fullStr Least squares data fitting
title_full_unstemmed Least squares data fitting
title_sort least squares data fitting
description  It is desired to represent, as good as possible, a series of data by means of certain functions with free parameters. "As good as possible" means that these parameters ara chosen so that the residuals, the difference between data and fitting functions, be as small as it is feasible. Our objective is not limited to finding the parameters of the best fit, but we also wish to know something about their uncertainties, this is, how well they are determined, given the errors of the original data as well as the imperfection of the fitting. Finally, supposing that we use the parameters of the fit in the calculation of other variables, we also want to have an estimation of the uncertainties of the latter. In order to do that, we imagine basic properties, wich we call "hypothesis", and then proceed from there with mathematical rigor. It is not superfluous to remember that the conclusions at wich we arrive depende on the hyphotheses done throughout the way, including the idea that useful information can be extracted from a least squares fit, of those data by these functions.
publisher Iniversidad Autónoma de Baja California
publishDate 2002
url https://www.cienciasmarinas.com.mx/index.php/cmarinas/article/view/204
_version_ 1715723941848285184

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