rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Nonlinear Least Squares for Inverse Problems
    sub title: Theoretical Foundations and Step-by-Step Guide for Applications
  name:
    name part: Chavent, Guy.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 360 p. online resource.
  abstract: 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 results, the applicability of various regularization techniques can be checked. The second objective of the book is to present frequent practical issues when solving NLS problems. Application oriented readers will find a detailed analysis of problems on the reduction to finite dimensions, the algebraic determination of derivatives (sensitivity functions versus adjoint method), the determination of the number of retrievable parameters, the choice of parametrization (multiscale, adaptive) and the optimization step, and the general organization of the inversion code. Special attention is paid to parasitic local minima, which can stop the optimizer far from the global minimum: multiscale parametrization is shown to be an efficient remedy in many cases, and a new condition is given to check both wellposedness and the absence of parasitic local minima. For readers that are interested in projection on non-convex sets, Part II of this book presents the geometric theory of quasi-convex and strictly quasi-convex (s.q.c.) sets. S.q.c. sets can be recognized by their finite curvature and limited deflection and possess a neighborhood where the projection is well-behaved. Throughout the book, each chapter starts with an overview of the presented concepts and results.
  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.
  note: by Guy Chavent.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical models
  subject:
    topic: Calculus of variations
  subject:
    topic: Physics
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Appl.Mathematics/Computational Methods of Engineering
  subject:
    topic: Calculus of Variations and Optimal Control; Optimization
  classification: TA342-343
  classification: 003.3
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Scientific Computation
  identifier: 9789048127856
  identifier: http://dx.doi.org/10.1007/978-90-481-2785-6
  record info:
    record creation date: 100715
    record change date: 20151204173114.0
    record identifier: 978-90-481-2785-6