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Least squares data fitting with applications /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Baltimore, Md. :
Johns Hopkins University Press,
2013.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 049 | |a UAMI | ||
| 100 | 1 | |a Hansen, Per Christian. | |
| 245 | 1 | 0 | |a Least squares data fitting with applications / |c Per Christian Hansen, Víctor Pereyra, Godela Scherer. |
| 260 | |a Baltimore, Md. : |b Johns Hopkins University Press, |c 2013. | ||
| 300 | |a 1 online resource (xv, 305 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a "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."--Publisher's website. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover -- Contents -- Preface -- Symbols and Acronyms -- 1 The Linear Data Fitting Problem -- 1.1 Parameter estimation, data approximation -- 1.2 Formulation of the data fitting problem -- 1.3 Maximum likelihood estimation -- 1.4 The residuals and their properties -- 1.5 Robust regression -- 2 The Linear Least Squares Problem -- 2.1 Linear least squares problem formulation -- 2.2 The QR factorization and its role -- 2.3 Permuted QR factorization -- 3 Analysis of Least Squares Problems -- 3.1 The pseudoinverse -- 3.2 The singular value decomposition | |
| 505 | 8 | |a 3.3 Generalized singular value decomposition3.4 Condition number and column scaling -- 3.5 Perturbation analysis -- 4 Direct Methods for Full-Rank Problems -- 4.1 Normal equations -- 4.2 LU factorization -- 4.3 QR factorization -- 4.4 Modifying least squares problems -- 4.5 Iterative refinement -- 4.6 Stability and condition number estimation -- 4.7 Comparison of the methods -- 5 Direct Methods for Rank-Deficient Problems -- 5.1 Numerical rank -- 5.2 Peters-Wilkinson LU factorization -- 5.3 QR factorization with column permutations | |
| 505 | 8 | |a 5.4 UTV and VSV decompositions5.5 Bidiagonalization -- 5.6 SVD computations -- 6 Methods for Large-Scale Problems -- 6.1 Iterative versus direct methods -- 6.2 Classical stationary methods -- 6.3 Non-stationary methods, Krylov methods -- 6.4 Practicalities: preconditioning and stopping criteria -- 6.5 Block methods -- 7 Additional Topics in Least Squares -- 7.1 Constrained linear least squares problems -- 7.2 Missing data problems -- 7.3 Total least squares (TLS) -- 7.4 Convex optimization -- 7.5 Compressed sensing -- 8 Nonlinear Least Squares Problems | |
| 505 | 8 | |a 8.1 Introduction8.2 Unconstrained problems -- 8.3 Optimality conditions for constrained problems -- 8.4 Separable nonlinear least squares problems -- 8.5 Multiobjective optimization -- 9 Algorithms for Solving Nonlinear LSQ Problems -- 9.1 Newton�s method -- 9.2 The Gauss-Newton method -- 9.3 The Levenberg-Marquardt method -- 9.4 Additional considerations and software -- 9.5 Iteratively reweighted LSQ algorithms for robust data fitting problems -- 9.6 Variable projection algorithm -- 9.7 Block methods for large-scale problems -- 10 Ill-Conditioned Problems | |
| 505 | 8 | |a 10.1 Characterization10.2 Regularization methods -- 10.3 Parameter selection techniques -- 10.4 Extensions of Tikhonov regularization -- 10.5 Ill-conditioned NLLSQ problems -- 11 Linear Least Squares Applications -- 11.1 Splines in approximation -- 11.2 Global temperatures data fitting -- 11.3 Geological surface modeling -- 12 Nonlinear Least Squares Applications -- 12.1 Neural networks training -- 12.2 Response surfaces, surrogates or proxies -- 12.3 Optimal design of a supersonic aircraft -- 12.4 NMR spectroscopy -- 12.5 Piezoelectric crystal identification | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Least squares. | |
| 650 | 0 | |a Mathematical models. | |
| 650 | 6 | |a Modèles mathématiques. | |
| 650 | 7 | |a mathematical models. |2 aat | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Least squares |2 fast | |
| 650 | 7 | |a Mathematical models |2 fast | |
| 650 | 7 | |a Statistik |2 gnd | |
| 650 | 7 | |a Methode der kleinsten Quadrate |2 gnd | |
| 650 | 7 | |a Modeles mathematiques. |2 ram | |
| 650 | 7 | |a Moindres carres |x Informatique. |2 ram | |
| 700 | 1 | |a Pereyra, V. |q (Victor) | |
| 700 | 1 | |a Scherer, Godela. | |
| 776 | 0 | 8 | |i Print version: |a Hansen, Per Christian. |t Least squares data fitting with applications. |d Baltimore, Md. : Johns Hopkins University Press, ©2013 |z 1421407868 |w (OCoLC)820530760 |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=601157 |z Texto completo |
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