[PDF] The Total Least Squares Problem eBook

Author : Sabine Van Huffel
Publisher : SIAM
Page : 302 pages
File Size : 21,21 MB
Release : 1991-01-01
Category : Mathematics
ISBN : 0898712750

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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.

Author : S. van Huffel
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 27,90 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 9401735522

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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.

Author : Charles L. Lawson
Publisher : SIAM
Page : 348 pages
File Size : 24,3 MB
Release : 1995-12-01
Category : Mathematics
ISBN : 0898713560

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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.

Author : James W. Demmel
Publisher : SIAM
Page : 426 pages
File Size : 24,89 MB
Release : 1997-08-01
Category : Mathematics
ISBN : 0898713897

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This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Author : Stephen Boyd
Publisher : Cambridge University Press
Page : 477 pages
File Size : 36,95 MB
Release : 2018-06-07
Category : Business & Economics
ISBN : 1316518965

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

Author : Sabine Van Huffel
Publisher : SIAM
Page : 313 pages
File Size : 20,76 MB
Release : 1991-01-01
Category : Mathematics
ISBN : 9781611971002

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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.

Author : Gene H. Golub
Publisher :
Page : 15 pages
File Size : 20,59 MB
Release : 1980
Category : Least squares
ISBN :

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Totla least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector $b (mxl)$ and in the data matrix $A (mxn)$. The technique has been discussed by several authors and amounts to fitting a "best" subspace to the points $(a[superscript]{T}_{i},b_{i}), i=1,\ldots,m,$ where $a[superscript]{T}_{i}$ is the $i$-th row of $A$. In this paper a singular value decomposition analysis of the TLS problem is presented. The sensitivity of the TLS problem as well as its relationship to ordinary least squares regression is explored. Aan algorithm for solving the TLS problem is proposed that utilizes the singular value decomposition and which provides a measure of the underlying problem's sensitivity.

Author : Sabine van Huffel
Publisher : SIAM
Page : 404 pages
File Size : 38,10 MB
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713930

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An overview of the computational issues; statistical, numerical, and algebraic properties, and new generalizations and applications of advances on TLS and EIV models. Experts from several disciplines prepared overview papers which were presented at the conference and are included in this book.

Author : Ake Bjorck
Publisher : SIAM
Page : 425 pages
File Size : 20,83 MB
Release : 1996-01-01
Category : Mathematics
ISBN : 9781611971484

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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
Page : 325 pages
File Size : 18,80 MB
Release : 2013-01-15
Category : Mathematics
ISBN : 1421408589

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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.