Least Squares Approximation
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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.
Introduction To Applied Linear Algebra
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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07
Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Least Squares Finite Element Methods
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Author : Pavel B. Bochev
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-28
Least Squares Finite Element Methods written by Pavel B. Bochev 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 2009-04-28 with Mathematics categories.
Since their emergence in the early 1950s, ?nite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of partial differential equations. At the time of their inception, ?nite e- ment methods were viewed primarily as a tool for solving problems in structural analysis. However, it did not take long to discover that ?nite element methods could be applied with equal success to problems in other engineering and scienti?c ?elds. Today, ?nite element methods are also in common use, and indeed are often the method of choice, for incompressible ?uid ?ow, heat transfer, electromagnetics, and advection-diffusion-reaction problems, just to name a few. Given the early conn- tion between ?nite element methods and problems engendered by energy minimi- tion principles, it is not surprising that the ?rst mathematical analyses of ?nite e- ment methods were given in the environment of the classical Rayleigh–Ritz setting. Yet again, using the fertile soil provided by functional analysis in Hilbert spaces, it did not take long for the rigorous analysis of ?nite element methods to be extended to many other settings. Today, ?nite element methods are unsurpassed with respect to their level of theoretical maturity.
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
Generalized Inverses
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Author : Adi Ben-Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Generalized Inverses written by Adi Ben-Israel 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 2006-04-18 with Mathematics categories.
This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.
Scattered Data Approximation
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Author : Holger Wendland
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-11
Scattered Data Approximation written by Holger Wendland and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-11 with Mathematics categories.
Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer aided geometric design, and meshless methods for partial differential equations.
Meshfree Approximation Methods With Matlab With Cd Rom
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Author : Gregory E Fasshauer
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-04-17
Meshfree Approximation Methods With Matlab With Cd Rom written by Gregory E Fasshauer and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-17 with Mathematics categories.
Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods.The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.
Econometric Methods With Applications In Business And Economics
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Author : Christiaan Heij
language : en
Publisher: OUP Oxford
Release Date : 2004-03-25
Econometric Methods With Applications In Business And Economics written by Christiaan Heij and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-25 with Business & Economics categories.
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.
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.
Approximation Theory And Methods
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Author : M. J. D. Powell
language : en
Publisher: Cambridge University Press
Release Date : 1981-03-31
Approximation Theory And Methods written by M. J. D. Powell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-03-31 with Mathematics categories.
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.