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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QA275 .H276 2013 | Unknown |
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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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