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: Lectures on Constructive Approximation
    sub title: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball
  name:
    name part: Michel, Volker.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 326 p. 7 illus., 5 illus. in color. online resource.
  abstract: Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelets and scaling functions This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.
  table of contents: Introduction: the Problem to be Solved -- Part I Basics -- Basic Fundamentals—What You Need to Know -- Approximation of Functions on the Real Line -- Part II Approximation on the Sphere -- Basic Aspects -- Fourier Analysis -- Spherical Splines -- Spherical Wavelet Analysis -- Spherical Slepian Functions -- Part III Approximation on the 3D Ball -- Orthonormal Bases -- Splines -- Wavelets for Inverse Problems on the 3D Ball -- The Regularized Functional Matching Pursuit (RFMP) -- References -- Index.
  note: by Volker Michel.
  subject:
    topic: Mathematics
  subject:
    topic: Approximation theory
  subject:
    topic: Fourier analysis
  subject:
    topic: Special functions
  subject:
    topic: Numerical analysis
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Special Functions
  subject:
    topic: Fourier Analysis
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Numerical Analysis
  classification: QA401-425
  classification: 511.4
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Applied and Numerical Harmonic Analysis
  identifier: 9780817684037
  identifier: http://dx.doi.org/10.1007/978-0-8176-8403-7
  record info:
    record creation date: 121211
    record change date: 20151204161644.0
    record identifier: 978-0-8176-8403-7