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Analytic approximation with real constraints, with applications to inverse diffusion problems
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J. Leblond
Published/Copyright:
March 5, 2008
The methods of constrained approximation in Hilbert spaces of analytic functions are applied to the solution of the inverse problems of detecting cracks or sources in a two-dimensional material by means of boundary measurements. Issues of well-posedness are discussed, and results on continuity and robustness with respect to the given data are established. Constructive and efficient methods for resolution of the above approximation problems are presented. The techniques are illustrated by numerical examples incorporating a further rational approximation step.
Keywords: Approximation; extremal problems; analytic functions; Hardy spaces; Toeplitz and Hankel operators; inverse problems
Received: 2006-March-06
Published Online: 2008-03-05
Published in Print: 2008-01
© de Gruyter
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Keywords for this article
Approximation;
extremal problems;
analytic functions;
Hardy spaces;
Toeplitz and Hankel operators;
inverse problems
Articles in the same Issue
- Inverse electromagnetic scattering by a perfect conductor in a chiral environment
- Recovering a potential from Cauchy data in the two-dimensional case
- Solving constraint ill-posed problems using Ginzburg–Landau regularization functionals
- An inverse problem of identifying source coefficient in solute transportation
- Boundary integral equations for acoustical inverse sound-soft scattering
- A note on logarithmic convergence rates for nonlinear Tikhonov regularization
- Analytic approximation with real constraints, with applications to inverse diffusion problems
