Least Squares Data Fitting with Applications

Inbunden, Engelska, 2013

AvPer Christian Hansen,Víctor Pereyra,Godela Scherer

1 459 kr

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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.

Produktinformation

Utgivningsdatum2013-03-12
Mått152 x 229 x 28 mm
Vikt567 g
FormatInbunden
SpråkEngelska
Antal sidor328
FörlagJohns Hopkins University Press
ISBN9781421407869

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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.

PrefaceSymbols and AcronymsChapter 1. The Linear Data Fitting Problem1.1. Parameter estimation, data approximation1.2. Formulation of the data fitting problem1.3. Maximum likelihood estimation1.4. The residuals and their properties1.5. Robust regressionChapter 2. The Linear Least Squares Problem2.1. Linear least squares problem formulation2.2. The QR factorization and its role2.3. Permuted QR factorizationChapter 3. Analysis of Least Squares Problems3.1. The pseudoinverse3.2. The singular value decomposition3.3. Generalized singular value decomposition3.4. Condition number and column scaling3.5. Perturbation analysisChapter 4. Direct Methods for Full-Rank Problems4.1. Normal equations4.2. LU factorization4.3. QR factorization4.4. Modifying least squares problems4.5. Iterative refinement4.6. Stability and condition number estimation4.7. Comparison of the methodsChapter 5. Direct Methods for Rank-Deficient Problems5.1. Numerical rank5.2. Peters-Wilkinson LU factorization5.3. QR factorization with column permutations5.4. UTV and VSV decompositions5.5. Bidiagonalization5.6. SVD computationsChapter 6. Methods for Large-Scale Problems6.1. Iterative versus direct methods6.2. Classical stationary methods6.3. Non-stationary methods, Krylov methods6.4. Practicalities: preconditioning and stopping criteria6.5. Block methodsChapter 7. Additional Topics in Least Squares7.1. Constrained linear least squares problems7.2. Missing data problems7.3. Total least squares (TLS)7.4. Convex optimization7.5. Compressed sensingChapter 8. Nonlinear Least Squares Problems8.1. Introduction8.2. Unconstrained problems8.3. Optimality conditions for constrained problems8.4. Separable nonlinear least squares problems8.5. Multiobjective optimizationChapter 9. Algorithms for Solving Nonlinear LSQ Problems9.1. Newton's method9.2. The Gauss-Newton method9.3. The Levenberg-Marquardt method9.4. Additional considerations and software9.5. Iteratively reweighted LSQ algorithms for robust data fitting problems9.6. Variable projection algorithm9.7. Block methods for large-scale problemsChapter 10. Ill-Conditioned Problems10.1. Characterization10.2. Regularization methods10.3. Parameter selection techniques10.4. Extensions of Tikhonov regularization10.5. Ill-conditioned NLLSQ problemsChapter 11. Linear Least Squares Applications11.1. Splines in approximation11.2. Global temperatures data fitting11.3. Geological surface modelingChapter 12. Nonlinear Least Squares Applications12.1. Neural networks training12.2. Response surfaces, surrogates or proxies12.3. Optimal design of a supersonic aircraft12.4. NMR spectroscopy12.5. Piezoelectric crystal identification12.6. Travel time inversion of seismic dataAppendix A: Sensitivity AnalysisA.1. Floating-point arithmeticA.2. Stability, conditioning and accuracyAppendix B: Linear Algebra BackgroundB.1. NormsB.2. Condition numberB.3. OrthogonalityB.4. Some additional matrix propertiesAppendix C: Advanced Calculus BackgroundC.1. Convergence ratesC.2. Multivariable calculusAppendix D: StatisticsD.1. DefinitionsD.2. Hypothesis testingReferencesIndex