Least squares data fitting with applications /

Mostrar otras versiones (2)

"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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hansen, Per Christian
Otros Autores: Pereyra, V. (Victor), Scherer, Godela
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Baltimore, Md. : Johns Hopkins University Press, 2013.
Colección:Book collections on Project MUSE.
Temas:
Least squares.
Mathematical models.
Modèles mathématiques.
mathematical models.
MATHEMATICS > General.
Least squares
Mathematical models
Statistik
Methode der kleinsten Quadrate
Modeles mathematiques.
Moindres carres > Informatique.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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
  • 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
  • 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 Newtonâ€?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
  • 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

Ejemplares similares