Least squares data fitting with applications

Responsibility Per Christian Hansen, Víctor Pereyra, Godela Scherer. Imprint Baltimore, Md. : Johns Hopkins University Press, 2013. Physical description xv, 305 p. : ill. ; 24 cm.

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Description

Creators/Contributors

Author/Creator Hansen, Per Christian. Contributor Pereyra, V. (Victor) Scherer, Godela.

Contents/Summary

• PrefaceSymbols and Acronym
• s1. 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 regressio
• n2. The Linear Least Squares Problem2
• .1. Linear least squares problem formulation2
• .2. The QR factorization and its role2
• .3. Permuted QR factorizatio
• n3. 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 analysi
• s4. 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 method
• s5. 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 computation
• s6. 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 method
• s7. 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 sensin
• g8. Nonlinear Least Squares Problems8
• .1. Introduction8
• .2. Unconstrained problems8
• .3. Optimality conditions for constrained problems8
• .4. Separable nonlinear least squares problems8
• .5. Multiobjective optimizatio
• n9. 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 problem
• s10. Ill-Conditioned Problems10
• .1. Characterization10
• .2. Regularization methods10
• .3. Parameter selection techniques10
• .4. Extensions of Tikhonov regularization10
• .5. Ill-conditioned NLLSQ problem
• s11. Linear Least Squares Applications11
• .1. Splines in approximation11
• .2. Global temperatures data fitting11
• .3. Geological surface modelin
• g12. 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.
• (source: Nielsen Book Data)

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