The Theory Of Errors And Method Of Least Squares
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The Theory Of Errors And Method Of Least Squares
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Author : William Woolsey Johnson
language : en
Publisher:
Release Date : 1892
The Theory Of Errors And Method Of Least Squares written by William Woolsey Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1892 with Error analysis (Mathematics) categories.
The Theory Of Errors And Method Of Least Squares
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Author : William Johnson
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2015-07-16
The Theory Of Errors And Method Of Least Squares written by William Johnson and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-16 with categories.
From the INTRODUCTORY. Errors of Observation. 1. A quantity of which the magnitude is to be determined is either directly measured, or, as in the more usual case, deduced by calculation from quantities which are directly measured. The result of a direct measurement is called an observation. Observations of the kind here considered are thus of the nature of readings upon some scale, generally attached to an instrument of observation. The least count of the instrument is the smallest difference recognized in the readings of the instrument, so that every observation is recorded as an integral multiple of the least count. 2. Repeated observations of the same quantity, even when made with the same instrument and apparently under the same circumstances, will nevertheless differ materially. An increase in the nicety of the observations, and the precision of the instrument, may decrease the discrepancies in actual magnitude; but at the same time, by diminishing the least count, their numerical measures will generally be increased; so that, with the most refined instruments, the discrepancies may amount to many times the least count. Thus every observation is subject to an error, the error being the difference between the observed value and the true value; an observed value which exceeds the true value is regarded as having a positive error, and one which falls short of it as having a negative error. 3. An error may be regarded as the algebraic sum of a number of elemental errors due to various causes. So far as these causes can be ascertained, their results are not errors at all, in the sense in which the term is here used, and are supposed to have been removed by means of proper corrections. Systematic errors are such as result from unknown causes affecting all the observations alike. These again are not the subjects of the "theory of errors," which is concerned solely with the accidental errors which produce the discrepancies between the observations.
The Theory Of Errors And Method Of Least Squares
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Author : William Woolsey Johnson
language : en
Publisher:
Release Date : 1909
The Theory Of Errors And Method Of Least Squares written by William Woolsey Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1909 with Error analysis (Mathematics) categories.
The Theory Of Errors And Method Of Least Squares
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Author : William Woolsey Johnson
language : en
Publisher:
Release Date : 2018-04-15
The Theory Of Errors And Method Of Least Squares written by William Woolsey Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-15 with categories.
The Theory Of Errors And Method Of Least Squares Classic Reprint
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Author : William Woolsey Johnson
language : en
Publisher:
Release Date : 2015-08-06
The Theory Of Errors And Method Of Least Squares Classic Reprint written by William Woolsey Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-06 with Mathematics categories.
Excerpt from The Theory of Errors and Method of Least Squares The basis adopted in this book for the theory of accidental errors is that laid down by Gauss in the Theoria Motus Corporum CaUstium (republished as vol. vii of the Werke) which may be described for the most part in his own words, as follows: "The hypothesis is in fact wont to be considered as an axiom that, if any quantity has been determined by several direct observations, made under similar circumstances and with equal care, the arithmetical mean between all the observed values presents the most probable value, if not with absolute rigor, at least very nearly so, so that it is always safest to adhere to it." (Art.177.) Then introducing the notion of a law of facility of error to give precise meaning to the phrase "most probable value," we cannot do better than to adopt that law of facility in accordance with which the arithmetical mean is the most probable value. After deriving this law and showing that it leads to the principle of least squares, he says: "This principle, which in all applications of mathematics to natural philosophy admits of very frequent use, ought everywhere to hold good as an axiom by the same right as that by which the arithmetical mean between several observed values of the same quantity is adopted as the most probable value." (Art. 179) About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
The Total Least Squares Problem
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Author : Sabine Van Huffel
language : en
Publisher: SIAM
Release Date : 1991-01-01
The Total Least Squares Problem written by Sabine Van Huffel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-01 with Mathematics categories.
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
Nbs Special Publication
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Author :
language : en
Publisher:
Release Date : 1918
Nbs Special Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1918 with Weights and measures categories.
Technical News Bulletin Of The National Bureau Of Standards
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Author :
language : en
Publisher:
Release Date : 1950
Technical News Bulletin Of The National Bureau Of Standards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1950 with Technology categories.
Theory Of Errors And Method Of Least Squares
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Author : Johnson William Woolsey
language : en
Publisher:
Release Date : 1901
Theory Of Errors And Method Of Least Squares written by Johnson William Woolsey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1901 with categories.
The Theory Of Errors And Method Of Least Squares
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Author : Willian Woolsey Johnson
language : en
Publisher: Palala Press
Release Date : 2016-05-09
The Theory Of Errors And Method Of Least Squares written by Willian Woolsey Johnson and has been published by Palala Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-09 with categories.
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.