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Download or read book A Text Book on the Method of Least Squares written by Mansfield Merriman and published by . This book was released on 1884 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Test-book on the Method of Least Squares written by Mansfield Merriman and published by . This book was released on 1907 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: John Wolberg
Publisher: Springer Science & Business Media
Published: 2006-02-08
Total Pages: 257
ISBN-13: 3540317201
DOWNLOAD EBOOKDevelops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods
Download or read book Data Analysis Using the Method of Least Squares written by John Wolberg and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods
Download or read book A test-book on The Method of Least Squares written by Mansfield Merriman and published by . This book was released on 1911 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Text-book on the Method of Least Squares ... written by Mansfield Merriman and published by . This book was released on 1924 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author: Ake Bjorck
Publisher: SIAM
Published: 1996-01-01
Total Pages: 425
ISBN-13: 9781611971484
DOWNLOAD EBOOKThe method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-01-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.
Author: Per Christian Hansen
Publisher: JHU Press
Published: 2013-01-15
Total Pages: 325
ISBN-13: 1421408589
DOWNLOAD EBOOKA lucid explanation of the intricacies of both simple and complex least squares methods. As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues. In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis that help readers to understand and evaluate the computed solutions • many examples that illustrate the techniques and algorithms Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.
Download or read book Least Squares Data Fitting with Applications written by Per Christian Hansen and published by JHU Press. This book was released on 2013-01-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid explanation of the intricacies of both simple and complex least squares methods. As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues. In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis that help readers to understand and evaluate the computed solutions • many examples that illustrate the techniques and algorithms Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.
Author: Mansfield Merriman
Publisher: Theclassics.Us
Published: 2013-09
Total Pages: 38
ISBN-13: 9781230859835
DOWNLOAD EBOOKThis historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 edition. Excerpt: ...weight. From remote antiquity the arithmetical mean of the measurements has always been regarded as the best or most probable value of the quantity sought; and, as shown in Art. 44, this is confirmed by the fundamental principle of the Method of Least Squares. Let z be the most probable value of the measured quantity, n the number of observations, and M any observation. Let r be the probable error of a single observation, and ra the probable error of the adjusted value z. Let also v be any residual obtained by subtracting M from z. The most probable value of the quantity is the arithmetical mean, expressed, as in Art. 44, by formula (8), z =. The probable error of a single observation, as shown in Art. 65, is, by formula (20), Lastly, as shown in Art. 64, the probable error of the mean is, by (19). r n Formula (8) indicates the method of adjustment, while (20) and (19) determine the precision of observation and of the mean. After finding z, each observation is subtracted from it, giving n values of v. The squares of these are taken, and their sum is Sz2; then r is computed, and lastly, r0. If desired, r0 can be also found directly from formula (21), which is the same as (19). 81. As an example, consider the following twenty-four measurements of an angle of the primary triangulation of the United-States Coast-Survey, made at the station Pocasset in Massachusetts, and recorded in the Report for 1854: --The most probable value of the angle is found by adding the observations, and dividing the sum by twenty-four. This is 116 43'49."64. Subtracting from this the first reading gives 5.19 for the first residual, which is placed in the column headed v. The square of this is 26.94, which is placed in the column headed v2. The sum of all these...
Download or read book A Text-Book on the Method of Least Squares written by Mansfield Merriman and published by Theclassics.Us. This book was released on 2013-09 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 edition. Excerpt: ...weight. From remote antiquity the arithmetical mean of the measurements has always been regarded as the best or most probable value of the quantity sought; and, as shown in Art. 44, this is confirmed by the fundamental principle of the Method of Least Squares. Let z be the most probable value of the measured quantity, n the number of observations, and M any observation. Let r be the probable error of a single observation, and ra the probable error of the adjusted value z. Let also v be any residual obtained by subtracting M from z. The most probable value of the quantity is the arithmetical mean, expressed, as in Art. 44, by formula (8), z =. The probable error of a single observation, as shown in Art. 65, is, by formula (20), Lastly, as shown in Art. 64, the probable error of the mean is, by (19). r n Formula (8) indicates the method of adjustment, while (20) and (19) determine the precision of observation and of the mean. After finding z, each observation is subtracted from it, giving n values of v. The squares of these are taken, and their sum is Sz2; then r is computed, and lastly, r0. If desired, r0 can be also found directly from formula (21), which is the same as (19). 81. As an example, consider the following twenty-four measurements of an angle of the primary triangulation of the United-States Coast-Survey, made at the station Pocasset in Massachusetts, and recorded in the Report for 1854: --The most probable value of the angle is found by adding the observations, and dividing the sum by twenty-four. This is 116 43'49."64. Subtracting from this the first reading gives 5.19 for the first residual, which is placed in the column headed v. The square of this is 26.94, which is placed in the column headed v2. The sum of all these...
Author: Mansfield Merriman
Publisher: Forgotten Books
Published: 2017-11-28
Total Pages: 244
ISBN-13: 9780332105222
DOWNLOAD EBOOKExcerpt from A Text-Book on the Method of Least Squares Independent observations may be either direct or indirect, but are subject to no rigorous conditions. Measurements on two of the angles of a triangle, for instance, are independent for the observed quantities can have no necessary geometrical dependence one upon the other. 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.
Download or read book A Text-Book on the Method of Least Squares (Classic Reprint) written by Mansfield Merriman and published by Forgotten Books. This book was released on 2017-11-28 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from A Text-Book on the Method of Least Squares Independent observations may be either direct or indirect, but are subject to no rigorous conditions. Measurements on two of the angles of a triangle, for instance, are independent for the observed quantities can have no necessary geometrical dependence one upon the other. 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.
Author: Mansfield Merriman
Publisher: Scholar's Choice
Published: 2015-02-17
Total Pages: 242
ISBN-13: 9781298109194
DOWNLOAD EBOOKThis 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.
Download or read book A Text Book on the Method of Least Squares - Scholar's Choice Edition written by Mansfield Merriman and published by Scholar's Choice. This book was released on 2015-02-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
