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

Larisa Beilina and Michael Victor Klibanov
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Larisa Beilina: Chalmers University of Technology Gothenburg University, Department of Mathematical Sciences
Michael Victor Klibanov: University of North Carolina

Chapter Chapter 1 in Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, 2012, pp 1-93 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4419-7805-9_1

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