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Unified approach to classical equations of inverse problem theory
-
Mikhail I. Belishev
und
Victor S. Mikhaylov
Veröffentlicht/Copyright:
2. Oktober 2012
Abstract.
The boundary control (BC) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of inverse problem theory (Gelfand–Levitan, Krein and Marchenko equations) can be derived in the framework of the BC method in a unified way. Namely, to solve each of these equations one has in fact to solve a relevant boundary control problem, whereas its solution is determined by the inverse data.
Received: 2012-06-05
Published Online: 2012-10-02
Published in Print: 2012-10-01
© 2012 by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
- Masthead
- Preface
- Single-logarithmic stability for the Calderón problem with local data
- The identification problem for the functional equation with a parameter
- A posteriori error analysis for unstable models
- A review of selected techniques in inverse problem nonparametric probability distribution estimation
- Unified approach to classical equations of inverse problem theory
- Optimized analytic reconstruction for SPECT
- Numerical method for solving an inverse electrocardiography problem for a quasi stationary case
- A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data
- On inverse problems in partially ordered spaces with a priori information
- An iterative method for a two-dimensional inverse scattering problem for a dielectric
- On the Shack–Hartmann based wavefront reconstruction: Stability and convergence rates of finite-dimensional approximations
- Unique continuation and continuous dependence results for a severely ill-posed integro-differential parabolic problem
Artikel in diesem Heft
- Masthead
- Preface
- Single-logarithmic stability for the Calderón problem with local data
- The identification problem for the functional equation with a parameter
- A posteriori error analysis for unstable models
- A review of selected techniques in inverse problem nonparametric probability distribution estimation
- Unified approach to classical equations of inverse problem theory
- Optimized analytic reconstruction for SPECT
- Numerical method for solving an inverse electrocardiography problem for a quasi stationary case
- A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data
- On inverse problems in partially ordered spaces with a priori information
- An iterative method for a two-dimensional inverse scattering problem for a dielectric
- On the Shack–Hartmann based wavefront reconstruction: Stability and convergence rates of finite-dimensional approximations
- Unique continuation and continuous dependence results for a severely ill-posed integro-differential parabolic problem
