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Two Central Questions of This Book and an Introduction to the Theories of Ill-posed and Coefficient Inverse Problems

  • Larisa Beilina
  • Michael Victor Klibanov
Chapter

Abstract

This is an introductory chapter. In Sect. 1.1, we outline two central questions discussed in this book. Sections 1.2–1.9 are introductory ones to the theory of illposed problems. In Sects. 1.10 and 1.11, we present main uniqueness results for coefficient inverse problems (CIPs) with the single measurement data. The material of this chapter might serve as an introductory course for theories of ill-posed and CIPs. We refer to books [7, 10, 41, 45, 48, 51, 54, 60, 65, 83, 84, 90, 93, 94, 102, 124, 138, 143, 144, 153, 154] where various Ill-Posed and CIPs were studied.

Keywords

Inverse Problem Regularization Parameter Uniqueness Theorem Central Question Tikhonov Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Larisa Beilina
    • 1
  • Michael Victor Klibanov
    • 2
  1. 1.Department of Mathematical SciencesChalmers University of Technology Gothenburg UniversityGothenburgSweden
  2. 2.University of North CarolinaCharlotteUSA

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