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Approximately Globally Convergent Numerical Method

In: Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems

Author

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  • Larisa Beilina

    (Chalmers University of Technology Gothenburg University, Department of Mathematical Sciences)

  • Michael Victor Klibanov

    (University of North Carolina)

Abstract

In this chapter, we present our approximately globally convergent numerical method for a multidimensional CIP for a hyperbolic PDE. This method also works for a similar CIP for a parabolic PDE. The numerical method of the current chapter addresses the first central question of this book (Sect. 1.1). The first publication about this method was [24] with follow-up works [25–29, 109, 114–117, 160]. We remind that only multidimensional CIPs with single measurement data are considered in this book. Recall that the term “single measurement” means that the boundary data are generated either by a single position of the point source or by a single direction of the initializing plane wave (Sect. 1.1.2). It will become clear from the material below that when approximately solving certain nonlinear integral differential equations with Volterra-like integrals, we use an analog of the wellknown predictor-corrector approach.

Suggested Citation

  • Larisa Beilina & Michael Victor Klibanov, 2012. "Approximately Globally Convergent Numerical Method," Springer Books, in: Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems, edition 127, chapter 0, pages 95-167, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-7805-9_2
    DOI: 10.1007/978-1-4419-7805-9_2
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