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Author : Open University. Linear Mathematics Course Team
Publisher : Unknown
Page : 52 pages
File Size : 47,8 Mb
Release : 1972
Category : Approximation theory
ISBN : PSU:000029909841
Author : Mansfield Merriman
Publisher : Unknown
Page : 214 pages
File Size : 50,5 Mb
Release : 1884
Category : Least squares
ISBN : NYPL:33433066412853
Author : Ake Bjorck
Publisher : SIAM
Page : 425 pages
File Size : 50,6 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 1611971489
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 : Ake Bjorck
Publisher : SIAM
Page : 421 pages
File Size : 54,6 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 9780898713602
The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.
Author : Sung Joon Ahn
Publisher : Springer
Page : 127 pages
File Size : 50,5 Mb
Release : 2004-10-29
Category : Computers
ISBN : 9783540286271
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.
Author : Per Christian Hansen,Víctor Pereyra,Godela Scherer
Publisher : JHU Press
Page : 325 pages
File Size : 42,6 Mb
Release : 2013-01-15
Category : Mathematics
ISBN : 9781421408583
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 : Wen Shen
Publisher : World Scientific
Page : 339 pages
File Size : 49,5 Mb
Release : 2019-08-28
Category : Mathematics
ISBN : 9789811204432
This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.
Author : Tilo Strutz
Publisher : Springer Vieweg
Page : 0 pages
File Size : 44,8 Mb
Release : 2015-12-16
Category : Technology & Engineering
ISBN : 365811455X
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
Author : Christiaan Heij,Paul de Boer,Philip Hans Franses,Teun Kloek,Herman K. van Dijk,All at the Erasmus University in Rotterdam
Publisher : OUP Oxford
Page : 816 pages
File Size : 55,9 Mb
Release : 2004-03-25
Category : Business & Economics
ISBN : 9780191608407
Nowadays applied work in business and economics requires a solid understanding of econometric methods to support decision-making. Combining a solid exposition of econometric methods with an application-oriented approach, this rigorous textbook provides students with a working understanding and hands-on experience of current econometrics. Taking a 'learning by doing' approach, it covers basic econometric methods (statistics, simple and multiple regression, nonlinear regression, maximum likelihood, and generalized method of moments), and addresses the creative process of model building with due attention to diagnostic testing and model improvement. Its last part is devoted to two major application areas: the econometrics of choice data (logit and probit, multinomial and ordered choice, truncated and censored data, and duration data) and the econometrics of time series data (univariate time series, trends, volatility, vector autoregressions, and a brief discussion of SUR models, panel data, and simultaneous equations). · Real-world text examples and practical exercise questions stimulate active learning and show how econometrics can solve practical questions in modern business and economic management. · Focuses on the core of econometrics, regression, and covers two major advanced topics, choice data with applications in marketing and micro-economics, and time series data with applications in finance and macro-economics. · Learning-support features include concise, manageable sections of text, frequent cross-references to related and background material, summaries, computational schemes, keyword lists, suggested further reading, exercise sets, and online data sets and solutions. · Derivations and theory exercises are clearly marked for students in advanced courses. This textbook is perfect for advanced undergraduate students, new graduate students, and applied researchers in econometrics, business, and economics, and for researchers in other fields that draw on modern applied econometrics.
Author : John Wolberg
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 42,9 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9783540317203
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
Author : Andrea Rott
Publisher : Herbert Utz Verlag
Page : 122 pages
File Size : 44,5 Mb
Release : 1999
Category : Electronic
ISBN : 3896755161
Author : Frank J. Zeleznik,Sanford Gordon
Publisher : Unknown
Page : 24 pages
File Size : 46,7 Mb
Release : 1961
Category : Approximation theory
ISBN : UIUC:30112106865329
Author : Dana Prescott Bartlett
Publisher : Unknown
Page : 290 pages
File Size : 47,6 Mb
Release : 1896
Category : Mathematics
ISBN : UCAL:C3118072
Author : Carl Friedrich Gauss
Publisher : Unknown
Page : 416 pages
File Size : 47,7 Mb
Release : 1857
Category : Orbits
ISBN : OXFORD:600015143
Author : Pavel B. Bochev,Max D. Gunzburger
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 51,6 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387689227
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.