Nonlinear Least Squares for Inverse Problems Theoretical Foundations and Step-by-Step Guide for Applications /

• Main Author: Chavent, Guy (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 2010.
• Series: Scientific Computation,
• Subjects: Mathematics.; Mathematical models.; Calculus of variations.; Physics.; Applied mathematics.; Engineering mathematics.; Mathematical Modeling and Industrial Mathematics.; Mathematical Methods in Physics.; Appl.Mathematics/Computational Methods of Engineering.; Calculus of Variations and Optimal Control; Optimization.

This book provides an introduction into the least squares resolution of nonlinear inverse problems. The first goal is to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, i.e. both wellposedness and optimizability. Using the...

Table of Contents:

• Nonlinear Least Squares
• Nonlinear Inverse Problems: Examples and Difficulties
• Computing Derivatives
• Choosing a Parameterization
• Output Least Squares Identifiability and Quadratically Wellposed NLS Problems
• Regularization of Nonlinear Least Squares Problems
• A generalization of convex sets
• Quasi-Convex Sets
• Strictly Quasi-Convex Sets
• Deflection Conditions for the Strict Quasi-convexity of Sets.