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Least Squares Data Fitting with Applications [Kõva köide]

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, , (Technical University of Denmark)
  • Formaat: Hardback, 328 pages, kõrgus x laius x paksus: 229x152x28 mm, kaal: 567 g, 9 Halftones, black and white; 46 Graphs; 8 Line drawings, black and white
  • Ilmumisaeg: 12-Mar-2013
  • Kirjastus: Johns Hopkins University Press
  • ISBN-10: 1421407868
  • ISBN-13: 9781421407869
Teised raamatud teemal:
Least Squares Data Fitting with ApplicationsSuurem pilt
  • Formaat: Hardback, 328 pages, kõrgus x laius x paksus: 229x152x28 mm, kaal: 567 g, 9 Halftones, black and white; 46 Graphs; 8 Line drawings, black and white
  • Ilmumisaeg: 12-Mar-2013
  • Kirjastus: Johns Hopkins University Press
  • ISBN-10: 1421407868
  • ISBN-13: 9781421407869
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781421407869.html
Märksõnad:
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, Victor 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; and 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.

Arvustused

Least Square Data fitting with Applications is a book that will be of great practical use to anyone whose work involves the analysis of data and its modeling. It offers a great deal of information that can be a s valuable in the lecture theater as in the lab or office. Mathematics Today

Muu info

Least squares remains a key topic in scientific computing, serving as a vital bridge between data and models. This book describes many interesting aspects of this problem class, including its statistical foundations, algorithms for solving both linear and nonlinear models, and its applications to many disciplines. The authors convey both the rich history of the subject and its ongoing importance. -- Stephen Wright, University of Wisconsin-Madison
Preface ix
Symbols and Acronyms xiii
1 The Linear Data Fitting Problem
1(24)
1.1 Parameter estimation, data approximation
1(3)
1.2 Formulation of the data fitting problem
4(5)
1.3 Maximum likelihood estimation
9(4)
1.4 The residuals and their properties
13(6)
1.5 Robust regression
19(6)
2 The Linear Least Squares Problem
25(22)
2.1 Linear least squares problem formulation
25(8)
2.2 The QR factorization and its role
33(6)
2.3 Permuted QR factorization
39(8)
3 Analysis of Least Squares Problems
47(18)
3.1 The pseudoinverse
47(3)
3.2 The singular value decomposition
50(4)
3.3 Generalized singular value decomposition
54(1)
3.4 Condition number and column scaling
55(3)
3.5 Perturbation analysis
58(7)
4 Direct Methods for Full-Rank Problems
65(26)
4.1 Normal equations
65(3)
4.2 LU factorization
68(2)
4.3 QR factorization
70(10)
4.4 Modifying least squares problems
80(5)
4.5 Iterative refinement
85(3)
4.6 Stability and condition number estimation
88(1)
4.7 Comparison of the methods
89(2)
5 Direct Methods for Rank-Deficient Problems
91(14)
5.1 Numerical rank
92(1)
5.2 Peters-Wilkinson LU factorization
93(1)
5.3 QR factorization with column permutations
94(4)
5.4 UTV and VSV decompositions
98(1)
5.5 Bidiagonalization
99(2)
5.6 SVD computations
101(4)
6 Methods for Large-Scale Problems
105(16)
6.1 Iterative versus direct methods
105(2)
6.2 Classical stationary methods
107(1)
6.3 Non-stationary methods, Krylov methods
108(6)
6.4 Practicalities: preconditioning and stopping criteria
114(3)
6.5 Block methods
117(4)
7 Additional Topics in Least Squares
121(26)
7.1 Constrained linear least squares problems
121(10)
7.2 Missing data problems
131(5)
7.3 Total least squares (TLS)
136(7)
7.4 Convex optimization
143(1)
7.5 Compressed sensing
144(3)
8 Nonlinear Least Squares Problems
147(16)
8.1 Introduction
147(3)
8.2 Unconstrained problems
150(6)
8.3 Optimality conditions for constrained problems
156(2)
8.4 Separable nonlinear least squares problems
158(2)
8.5 Multiobjective optimization
160(3)
9 Algorithms for Solving Nonlinear LSQ Problems
163(28)
9.1 Newton's method
164(2)
9.2 The Gauss-Newton method
166(4)
9.3 The Levenberg-Marquardt method
170(6)
9.4 Additional considerations and software
176(2)
9.5 Iteratively reweighted LSQ algorithms for robust data fitting problems
178(3)
9.6 Variable projection algorithm
181(5)
9.7 Block methods for large-scale problems
186(5)
10 Ill-Conditioned Problems
191(12)
10.1 Characterization
191(1)
10.2 Regularization methods
192(3)
10.3 Parameter selection techniques
195(3)
10.4 Extensions of Tikhonov regularization
198(3)
10.5 Ill-conditioned NLLSQ problems
201(2)
11 Linear Least Squares Applications
203(28)
11.1 Splines in approximation
203(9)
11.2 Global temperatures data fitting
212(9)
11.3 Geological surface modeling
221(10)
12 Nonlinear Least Squares Applications
231(32)
12.1 Neural networks training
231(7)
12.2 Response surfaces, surrogates or proxies
238(3)
12.3 Optimal design of a supersonic aircraft
241(7)
12.4 NMR spectroscopy
248(3)
12.5 Piezoelectric crystal identification
251(7)
12.6 Travel time inversion of seismic data
258(5)
Appendix A Sensitivity Analysis
263(4)
A.1 Floating-point arithmetic
263(1)
A.2 Stability, conditioning and accuracy
264(3)
Appendix B Linear Algebra Background
267(4)
B.1 Norms
267(1)
B.2 Condition number
268(1)
B.3 Orthogonality
269(1)
B.4 Some additional matrix properties
270(1)
Appendix C Advanced Calculus Background
271(4)
C.1 Convergence rates
271(1)
C.2 Multivariate calculus
272(3)
Appendix D Statistics
275(6)
D.1 Definitions
275(5)
D.2 Hypothesis testing
280(1)
References 281(20)
Index 301
Per Christian Hansen is a professor of scientific computing at the Technical University of Denmark. Victor Pereyra is a consulting professor of energy resources engineering at Stanford University and was a principal at Weidlinger Associates, Los Altos, California. Godela Scherer is a visiting research fellow in the Department of Mathematics at the University of Reading, United Kingdom, and a professor of scientific computing at the Universidad Simon Bolivar, Venezuela.