method of least square वाक्य
उदाहरण वाक्य
मोबाइल
- To bring them into agreement, the small inconsistencies ( usually only a few cm ) are adjusted using the method of least squares that is, eliminated in a statistically plausible manner.
- These equations are solved by the method of least squares which minimizes the sum of the squares of the differences between the observed and calculated arrival times, and a new estimated hypocenter is computed.
- Important papers of his include " On series expansions determined by the methods of least squares ", and " Investigations of the number of primes less than a given number ".
- When the name is used, the " Gaussian distribution " was named after Carl Friedrich Gauss, who introduced the distribution in 1809 as a way of rationalizing the method of least squares as outlined above.
- In 1810, after reading Gauss's work, Laplace, after proving the central limit theorem, used it to give a large sample justification for the method of least square and the normal distribution.
- The method of least squares leads to a consideration of problems in an inner product space, involving projection onto subspaces, and thus the problem of minimizing the squared errors can be reduced to a problem in numerical linear algebra.
- The minor planet was named in memory of Finnish scientist Henrik Johan Walbeck ( 1793 1822 ), astronomer and geodesist at the old Academia Aboensis who used the method of least squares to derive a good value for the Earth's flattening.
- When the method of least squares is used to estimate " ? " 0 and ? 1, then the residuals \ scriptstyle \ widehat \ varepsilon, unlike the errors \ scriptstyle \ varepsilon, cannot be independent since they satisfy the two constraints
- Adrain, Gauss, and Legendre all motivated the method of least squares by the problem of reconciling disparate physical measurements; in the case of Gauss and Legendre, the measurements in question were astronomical, and in Adrain's case they were survey measurements.
- :Assuming that the application of physics is correct ( I don't understand the " experimental " set-up ), and that the measurements are subject to about the same ( normal ) error distribution with ? = 0, the method of least squares is applicable and appropriate.
- In 1809 Gauss published his monograph " " Theoria motus corporum coelestium in sectionibus conicis solem ambientium " " where among other things he introduces several important statistical concepts, such as the method of least squares, the method of maximum likelihood, and the " normal distribution ".
- Meanwhile, the famous mathematician Carl Friedrich Gauss was entrusted from 1821 to 1825 with the triangulation of the kingdom of Hanover, for which he developed the method of least squares to find the best fit solution for problems of large systems of simultaneous equations given more real-world measurements than unknowns.
- Finally in 1812, Pierre-Simon Laplace published his " Th�orie analytique des probabilit�s " in which he consolidated and laid down many fundamental results in probability and statistics such as the moment generating function, method of least squares, inductive probability, and hypothesis testing, thus completing the final phase in the development of classical probability.
- Upon these follow special methods of induction applicable to quantity : the method of curves, the method of means, the method of least squares and the method of residues, and special methods depending on resemblance ( to which the transition is made through the law of continuity ), such as the method of gradation and the method of natural classification.
- These included attempts at the automation of observations ( appealing to the presumed objectivity of machines ), training observers to try to avoid certain known errors ( such as those caused by lack of sleep ), developing machines that could allow multiple observers to make observations at the same time, the taking of redundant data and using techniques such as the method of least squares to derive possible values from them, and trying to quantify the biases of individual workers so that they could be subtracted from the data.
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