Princeton University Library Catalog

Inverse scattering theory and transmission eigenvalues / Fioralba Cakoni, Rutgers University, Piscataway, New Jersey, David Colton, University of Delaware, Newark, Delaware, Houssem Haddar, INRIA and Ecole Polytechnique, Palaiseau, France.

Cakoni, Fioralba [Browse]
Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), [2016]
1 online resource (x, 183 pages).
  • CBMS-NSF regional conference series in applied mathematics ; 88. [More in this series]
  • CBMS-NSF regional conference series in applied mathematics ; 88
Summary note:
Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance. Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues.
Bibliographic references:
Includes bibliographical references and index.
Source of description:
Description based on title page of print version.
Preface -- 1. Inverse scattering theory -- 2. The determination of the support of inhomogeneous media -- 3. The interior transmission problem -- 4. The existence of transmission eigenvalues -- 5. Inverse spectral problems for transmission eigenvalues.
  • 9781611974461 electronic
  • print
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