Least Squares Data Fitting With Applications

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Least Squares Data Fitting with Applications

Per Christian Hansen,Víctor Pereyra,Godela Scherer
Least Squares Data Fitting with Applications Book PDF

Author : Per Christian Hansen,Víctor Pereyra,Godela Scherer
Publisher : JHU Press
Page : 325 pages
File Size : 44,8 Mb
Release : 2013-01-15
Category : Mathematics
ISBN : 9781421408583

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Least Squares Data Fitting with Applications by Per Christian Hansen,Víctor Pereyra,Godela Scherer Pdf

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.

Data Fitting and Uncertainty

Tilo Strutz
Data Fitting and Uncertainty Book PDF

Author : Tilo Strutz
Publisher : Springer Vieweg
Page : 0 pages
File Size : 49,6 Mb
Release : 2015-12-16
Category : Technology & Engineering
ISBN : 365811455X

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Data Fitting and Uncertainty by Tilo Strutz Pdf

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

A Least Squares Curve Fitting Method with Applications to the Calculation of Stability Coefficients from Transient-response Data

Marvin Shinbrot
A Least Squares Curve Fitting Method with Applications to the Calculation of Stability Coefficients from Transient response Data Book PDF

Author : Marvin Shinbrot
Publisher : Unknown
Page : 60 pages
File Size : 47,9 Mb
Release : 1951
Category : Differential equations, Linear
ISBN : UOM:39015086495390

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A Least Squares Curve Fitting Method with Applications to the Calculation of Stability Coefficients from Transient-response Data by Marvin Shinbrot Pdf

A least-squares method for calculating coefficients from a linear differential equation directly from transient-response data is presented. Examples illustrating the application of the method to the calculation of aircraft-stability parameters from the airplane response of an elevator deflection are given.

Exponential Data Fitting and Its Applications

Victor Pereyra,Godela Scherer
Exponential Data Fitting and Its Applications Book PDF

Author : Victor Pereyra,Godela Scherer
Publisher : Bentham Science Publishers
Page : 206 pages
File Size : 43,7 Mb
Release : 2010
Category : Computers
ISBN : 9781608050482

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Exponential Data Fitting and Its Applications by Victor Pereyra,Godela Scherer Pdf

"Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision a"

General Principles of the Method of Least Squares

Dana Prescott Bartlett
General Principles of the Method of Least Squares Book PDF

Author : Dana Prescott Bartlett
Publisher : Kessinger Publishing
Page : 160 pages
File Size : 43,6 Mb
Release : 2008-10-01
Category : Law
ISBN : 1437059619

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General Principles of the Method of Least Squares by Dana Prescott Bartlett Pdf

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Fitting Equations to Data

Cuthbert Daniel,Fred S. Wood,John Wayne Gorman
Fitting Equations to Data Book PDF

Author : Cuthbert Daniel,Fred S. Wood,John Wayne Gorman
Publisher : Wiley-Interscience
Page : 488 pages
File Size : 52,6 Mb
Release : 1980-04-25
Category : Mathematics
ISBN : UCSD:31822028745347

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Fitting Equations to Data by Cuthbert Daniel,Fred S. Wood,John Wayne Gorman Pdf

Helps any serious data analyst with a computer to recognize the strengths and limitations of data, to test the assumptions implicit in the least squares methods used to fit the data, to select appropriate forms of the variables, to judge which combinations of variables are most influential, and to state the conditions under which the fitted equations are applicable. This edition includes numerous extensions and new devices such as component and component-plus-residual plots, cross verification with a second sample, and an index of required x-precision; also, the search for better subset equations is enlarged to cover 262,144 alternatives. The methods described have been applied in agricultural, environmental, management, marketing, medical, physical, and social sciences. Mathematics is kept to the level of college algebra.

Data Fitting in the Chemical Sciences

Peter Gans
Data Fitting in the Chemical Sciences Book PDF

Author : Peter Gans
Publisher : John Wiley & Sons
Page : 280 pages
File Size : 40,5 Mb
Release : 1992-07-27
Category : Mathematics
ISBN : STANFORD:36105000076815

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Data Fitting in the Chemical Sciences by Peter Gans Pdf

Data Fitting in the Chemical Sciences Peter Gans, School of Chemistry, The University of Leeds, Leeds, UK Data fitting is a technique of central importance in modern experimental science. It is the means by which data is tested against a model of the experimental system, be it a theoretical or empirical model. In this book an all-round approach is adopted in which the first stage of data-fitting is seen as data collection, the second is numerical processing and the third a critical evaluation of the 'goodness' of fit in both statistical and common sense terms. Each stage is considered in detail: the sources and nature of experimental errors; the theory of least-squares fitting; probability theory; hypothesis testing, and the application of scientific criteria. The theory is complemented by three chapters on a wide range of applications. The emphasis of this book is on methodology: why certain procedures are preferred rather than how any one procedure is implemented. The author aims to assist people in extracting from their data its full information content, i.e. to use their data, not abuse it.

Data Analysis Using the Method of Least Squares

John Wolberg
Data Analysis Using the Method of Least Squares Book PDF

Author : John Wolberg
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 44,8 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9783540317203

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Data Analysis Using the Method of Least Squares by John Wolberg Pdf

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

OpenIntro Statistics

David Diez,Christopher Barr,Mine Çetinkaya-Rundel
OpenIntro Statistics Book PDF

Author : David Diez,Christopher Barr,Mine Çetinkaya-Rundel
Publisher : Unknown
Page : 128 pages
File Size : 51,9 Mb
Release : 2015-07-02
Category : Electronic
ISBN : 1943450048

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OpenIntro Statistics by David Diez,Christopher Barr,Mine Çetinkaya-Rundel Pdf

The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources.

Data Fitting and Uncertainty

Tilo Strutz
Data Fitting and Uncertainty Book PDF

Author : Tilo Strutz
Publisher : Vieweg+Teubner Verlag
Page : 0 pages
File Size : 51,6 Mb
Release : 2010-09-30
Category : Technology & Engineering
ISBN : 3834810223

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Data Fitting and Uncertainty by Tilo Strutz Pdf

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

Total Least Squares and Errors-in-Variables Modeling

S. van Huffel,P. Lemmerling
Total Least Squares and Errors in Variables Modeling Book PDF

Author : S. van Huffel,P. Lemmerling
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 54,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401735520

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Total Least Squares and Errors-in-Variables Modeling by S. van Huffel,P. Lemmerling Pdf

In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prepare an overview paper and present it at the third international workshop on TLS and EIV modeling held in Leuven, Belgium, August 27-29, 2001. These invited papers, representing two-thirds of the book, together with a selection of other presented contributions yield a complete overview of the main scientific achievements since 1996 in TLS and Errors-In-Variables modeling. In this way, the book nicely completes two earlier books on TLS (SIAM 1991 and 1997). Not only computational issues, but also statistical, numerical, algebraic properties are described, as well as many new generalizations and applications. Being aware of the growing interest in these techniques, it is a strong belief that this book will aid and stimulate users to apply the new techniques and models correctly to their own practical problems.

Numerical Methods for Least Squares Problems

Ake Bjorck
Numerical Methods for Least Squares Problems Book PDF

Author : Ake Bjorck
Publisher : SIAM
Page : 425 pages
File Size : 40,7 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 1611971489

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Numerical Methods for Least Squares Problems by Ake Bjorck Pdf

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.

Introduction to Applied Linear Algebra

Stephen Boyd,Lieven Vandenberghe
Introduction to Applied Linear Algebra Book PDF

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 52,9 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

IPython Interactive Computing and Visualization Cookbook

Cyrille Rossant
IPython Interactive Computing and Visualization Cookbook Book PDF

Author : Cyrille Rossant
Publisher : Packt Publishing Ltd
Page : 512 pages
File Size : 43,7 Mb
Release : 2014-09-25
Category : Computers
ISBN : 9781783284825

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IPython Interactive Computing and Visualization Cookbook by Cyrille Rossant Pdf

Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.

Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space

Sung Joon Ahn
Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space Book PDF

Author : Sung Joon Ahn
Publisher : Springer
Page : 127 pages
File Size : 50,7 Mb
Release : 2004-10-29
Category : Computers
ISBN : 9783540286271

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Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space by Sung Joon Ahn Pdf

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-fit’ algorithms for general curves and surfaces in space which are employed in the Fraunhofer software.