The Total Least Squares Problem

Author : Sabine Van Huffel
Publisher : SIAM
ISBN 13 : 0898712750
Total Pages : 302 pages
Book Rating : 4.59/5 ( download)

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Download or read book The Total Least Squares Problem written by Sabine Van Huffel and published by SIAM. This book was released on 1991-01-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9401735522
Total Pages : 389 pages
Book Rating : 4.20/5 ( download)

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Download or read book Total Least Squares and Errors-in-Variables Modeling written by S. van Huffel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : James W. Demmel
Publisher : SIAM
ISBN 13 : 0898713897
Total Pages : 426 pages
Book Rating : 4.93/5 ( download)

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Download or read book Applied Numerical Linear Algebra written by James W. Demmel and published by SIAM. This book was released on 1997-08-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

Author : Ake Bjorck
Publisher : SIAM
ISBN 13 : 9781611971484
Total Pages : 425 pages
Book Rating : 4.89/5 ( download)

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Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-01-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.60/5 ( download)

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Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Author : Christiaan Heij
Publisher : OUP Oxford
ISBN 13 : 0191608408
Total Pages : 816 pages
Book Rating : 4.07/5 ( download)

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Download or read book Econometric Methods with Applications in Business and Economics written by Christiaan Heij and published by OUP Oxford. This book was released on 2004-03-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Per Christian Hansen
Publisher : JHU Press
ISBN 13 : 1421408589
Total Pages : 325 pages
Book Rating : 4.83/5 ( download)

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Download or read book Least Squares Data Fitting with Applications written by Per Christian Hansen and published by JHU Press. This book was released on 2013-01-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gene H. Golub
Publisher : Princeton University Press
ISBN 13 : 1400833884
Total Pages : 376 pages
Book Rating : 4.87/5 ( download)

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Download or read book Matrices, Moments and Quadrature with Applications written by Gene H. Golub and published by Princeton University Press. This book was released on 2009-12-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

Author : Jan R. Magnus
Publisher : John Wiley & Sons
ISBN 13 : 1119541166
Total Pages : 633 pages
Book Rating : 4.65/5 ( download)

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Download or read book Matrix Differential Calculus with Applications in Statistics and Econometrics written by Jan R. Magnus and published by John Wiley & Sons. This book was released on 2019-03-15 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference. Fulfills the need for an updated and unified treatment of matrix differential calculus Contains many new examples and exercises based on questions asked of the author over the years Covers new developments in field and features new applications Written by a leading expert and pioneer of the theory Part of the Wiley Series in Probability and Statistics Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.

Author : Sabine van Huffel
Publisher : SIAM
ISBN 13 : 9780898713930
Total Pages : 404 pages
Book Rating : 4.35/5 ( download)

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Download or read book Recent Advances in Total Least Squares Techniques and Errors-in-variables Modeling written by Sabine van Huffel and published by SIAM. This book was released on 1997-01-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.