Least Squares Data Fitting With Applications
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Least Squares Data Fitting With Applications
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Author : Per Christian Hansen
language : en
Publisher: JHU Press
Release Date : 2013-01-15
Least Squares Data Fitting With Applications written by Per Christian Hansen and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-15 with Mathematics categories.
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 algorithmsLeast 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.
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.
Data Fitting And Uncertainty
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Author : Tilo Strutz
language : en
Publisher: Springer Vieweg
Release Date : 2015-12-16
Data Fitting And Uncertainty written by Tilo Strutz and has been published by Springer Vieweg this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-16 with Technology & Engineering categories.
The subject of data fitting bridges many disciplines, especially those traditionally dealing with statistics like physics, mathematics, engineering, biology, economy, or psychology, but also more recent fields like computer vision. This book addresses itself to engineers and computer scientists or corresponding undergraduates who are interested in data fitting by the method of least-squares approximation, but have no or only limited pre-knowledge in this field. Experienced readers will find in it new ideas or might appreciate the book as a useful work of reference. Familiarity with basic linear algebra is helpful though not essential as the book includes a self-contained introduction and presents the method in a logical and accessible fashion. The primary goal of the text is to explain how data fitting via least squares works. The reader will find that the emphasis of the book is on practical matters, not on theoretical problems. In addition, the book enables the reader to design own software implementations with application-specific model functions based on the comprehensive discussion of several examples. The text is accompanied with working source code in ANSI-C for fitting with weighted least squares including outlier detection. Among others the book covers following topics * fitting of linear and nonlinear functions with one- or multi-dimensional variables * weighted least-squares * outlier detection * evaluation of the fitting results * different optimisation strategies * combined fitting of different model functions * total least-squares approach with multi-dimensional conditions
Least Squares Orthogonal Distance Fitting Of Curves And Surfaces In Space
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Author : Sung Joon Ahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-12-07
Least Squares Orthogonal Distance Fitting Of Curves And Surfaces In Space written by Sung Joon Ahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-07 with Computers categories.
Due to the continuing progress of sensor technology, the availability of 3-D cameras is already foreseeable. These cameras are capable of generating a large set of measurement points within a very short time. There are a variety of 3-D camera applications in the fields of robotics, rapid product development and digital factories. In order to not only visualize the point cloud but also to recognize 3-D object models from the point cloud and then further process them in CAD systems, efficient and stable algorithms for 3-D information processing are required. For the automatic segmentation and recognition of such geometric primitives as plane, sphere, cylinder, cone and torus in a 3-D point cloud, efficient software has recently been developed at the Fraunhofer IPA by Sung Joon Ahn. This book describes in detail the complete set of ‘best-?t’ algorithms for general curves and surfaces in space which are employed in the Fraunhofer software.
Regression Analysis
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Author : Ashish Sen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Regression Analysis written by Ashish Sen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Psychology categories.
Any method of fitting equations to data may be called regression. Such equations are valuable for at least two purposes: making predictions and judging the strength of relationships. Because they provide a way of em pirically identifying how a variable is affected by other variables, regression methods have become essential in a wide range of fields, including the social sciences, engineering, medical research and business. Of the various methods of performing regression, least squares is the most widely used. In fact, linear least squares regression is by far the most widely used of any statistical technique. Although nonlinear least squares is covered in an appendix, this book is mainly about linear least squares applied to fit a single equation (as opposed to a system of equations). The writing of this book started in 1982. Since then, various drafts have been used at the University of Toronto for teaching a semester-long course to juniors, seniors and graduate students in a number of fields, including statistics, pharmacology, engineering, economics, forestry and the behav ioral sciences. Parts of the book have also been used in a quarter-long course given to Master's and Ph.D. students in public administration, urban plan ning and engineering at the University of Illinois at Chicago (UIC). This experience and the comments and criticisms from students helped forge the final version.
Solving Least Squares Problems
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Author : Charles L. Lawson
language : en
Publisher: SIAM
Release Date : 1995-12-01
Solving Least Squares Problems written by Charles L. Lawson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-01 with Mathematics categories.
This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.
Circular And Linear Regression
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Author : Nikolai Chernov
language : en
Publisher: CRC Press
Release Date : 2010-06-22
Circular And Linear Regression written by Nikolai Chernov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-22 with Computers categories.
Find the right algorithm for your image processing applicationExploring the recent achievements that have occurred since the mid-1990s, Circular and Linear Regression: Fitting Circles and Lines by Least Squares explains how to use modern algorithms to fit geometric contours (circles and circular arcs) to observed data in image processing and comput
Linear Models And Generalizations
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Author : C. Radhakrishna Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-15
Linear Models And Generalizations written by C. Radhakrishna Rao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-15 with Mathematics categories.
Thebookisbasedonseveralyearsofexperienceofbothauthorsinteaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and o?ers a selectionofclassicalandmodernalgebraicresultsthatareusefulinresearch work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss fu- tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and a variety of practical applications will be useful not only to students but also to researchers and consultants in statistics.
Applied Regression Analysis
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Author : John O. Rawlings
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-31
Applied Regression Analysis written by John O. Rawlings and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-31 with Mathematics categories.
Least squares estimation, when used appropriately, is a powerful research tool. A deeper understanding of the regression concepts is essential for achieving optimal benefits from a least squares analysis. This book builds on the fundamentals of statistical methods and provides appropriate concepts that will allow a scientist to use least squares as an effective research tool. Applied Regression Analysis is aimed at the scientist who wishes to gain a working knowledge of regression analysis. The basic purpose of this book is to develop an understanding of least squares and related statistical methods without becoming excessively mathematical. It is the outgrowth of more than 30 years of consulting experience with scientists and many years of teaching an applied regression course to graduate students. Applied Regression Analysis serves as an excellent text for a service course on regression for non-statisticians and as a reference for researchers. It also provides a bridge between a two-semester introduction to statistical methods and a thoeretical linear models course. Applied Regression Analysis emphasizes the concepts and the analysis of data sets. It provides a review of the key concepts in simple linear regression, matrix operations, and multiple regression. Methods and criteria for selecting regression variables and geometric interpretations are discussed. Polynomial, trigonometric, analysis of variance, nonlinear, time series, logistic, random effects, and mixed effects models are also discussed. Detailed case studies and exercises based on real data sets are used to reinforce the concepts. The data sets used in the book are available on the Internet.
Fitting Models To Biological Data Using Linear And Nonlinear Regression
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Author : Harvey Motulsky
language : en
Publisher: Oxford University Press
Release Date : 2004-05-27
Fitting Models To Biological Data Using Linear And Nonlinear Regression written by Harvey Motulsky and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-27 with Mathematics categories.
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.