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## English translation: least squares [method of]

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
 Spanish term or phrase: minimos cuadrados English translation: least squares [method of] Entered by:

 08:38 Sep 16, 2001
Spanish to English translations [PRO]
Tech/Engineering
 Spanish term or phrase: minimos cuadrados As in "Métodos de procesamiento en tiempo real y post levantamiento sobre la base de estimación de métodos de mínimos cuadrados". The context is an offshore seismic survey. (This is an item under the heading of Technical Features.)
 Local time: 18:48
 least squares [method of] Explanation:The "method of least squares" is commonly used in mathematics as applied to estimates in the various pure and applied sciences, including seismology. Google: http://www.google.com/search?q="method +of least squares"&bt... Specifically: http://www-star.stanford.edu/~mfuelle/gauss.html The Gaussian method of least sqaures The Gaussian method of least squares solves overdetermined linear system of equations by reducing the misfit between the observations y and the expected ones (G a) to its minimal value. This misfit may be described as the sum of squared residuals So representing the first term of the autocovariance function rho of the residuals r . To find the minimum of this quantity, the gradient with respect to the model parameters a is set to zero. This step impresses boundary conditions onto the original system, leading to the so called normal equations from which the estimated model parameters are found by matrix inversion. In this way the sum of squared residuals is minimized. This approach is valid if and only if the matrix G is noise free. But when replacing the nonlinear functional F by its linearized version G an error may be introduced either due to the deviation from linearity, discreteness, or by approaching the analytical description of G by means of uncertain measurements. This error results in a noisy matrix G and a biased solution for the model parameters a . If each column of the matrix G and the resolution vector y of the overdetermined linear system of equations has the same variance, the maximum likelihood method can be applied. In the more general case of completely independent variances, the minimization of correlated residuals is appropriate to the problem. --------------------------------------------------------------------------------
Selected response from:

DR. RICHARD BAVRY
 I will probably never receive an answer to any question as authoritative as yours to this one. Thank you.4 KudoZ points were awarded for this answer

5least squares [method of]DR. RICHARD BAVRY
5 -1method of squared minimums
 Parrot

10 mins   confidence: peer agreement (net): -1
method of squared minimums

Explanation:
A Spanish university syllabus in English on this method may be found below:

Reference: http://www.uc3m.es/uc3m/gral/ES/ESCU2/5211121.html
 ParrotSpainLocal time: 02:48Native speaker of: EnglishPRO pts in pair: 7645

disagree  DR. RICHARD BAVRY: sorry, Cecilia, but no such phrase "legitimately" exists in English.
 3 hrs

3 hrs   confidence:
least squares [method of]

Explanation:
The "method of least squares" is commonly used in mathematics as applied to estimates in the various pure and applied sciences, including seismology.

Specifically:

http://www-star.stanford.edu/~mfuelle/gauss.html
The Gaussian method of least sqaures
The Gaussian method of least squares solves overdetermined linear system of equations by reducing the misfit between the observations y and the expected ones (G a) to its minimal value. This misfit may be described as the sum of squared residuals So

representing the first term of the autocovariance function rho of the residuals r . To find the minimum of this quantity, the gradient with respect to the model parameters a is set to zero.

This step impresses boundary conditions onto the original system, leading to the so called normal equations from which the estimated model parameters are found by matrix inversion. In this way the sum of squared residuals is minimized.
This approach is valid if and only if the matrix G is noise free. But when replacing the nonlinear functional F by its linearized version G an error may be introduced either due to the deviation from linearity, discreteness, or by approaching the analytical description of G by means of uncertain measurements. This error results in a noisy matrix G and a biased solution for the model parameters a . If each column of the matrix G and the resolution vector y of the overdetermined linear system of equations has the same variance, the maximum likelihood method can be applied. In the more general case of completely independent variances, the minimization of correlated residuals is appropriate to the problem.
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See above, plus I have been an organic chemist for 30 years
 DR. RICHARD BAVRYPRO pts in pair: 94
 I will probably never receive an answer to any question as authoritative as yours to this one. Thank you.