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Reconstruction techniques for classical inverse Sturm-Liouville problems
This paper gives constructive algorithms for the classical inverse Sturm-Liouville problem. It is shown that many of the formulations of this problem are equivalent to solving an overdeterminedExpand
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Iterative methods for the reconstruction of an inverse potential problem
This paper considers an inverse potential problem which seeks to recover the shape of an obstacle separating two different densities by measurements of the potential. A representation for the domainExpand
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A Second Degree Method for Nonlinear Inverse Problems
The paper is concerned with the solution of nonlinear ill-posed problems by methods that utilize the second derivative. Expand
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Nonlinear integral equations and the iterative solution for an inverse boundary value problem
Determining the shape of a perfectly conducting inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modelled as an inverseExpand
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Inverse Obstacle Scattering with Modulus of the Far Field Pattern as Data
For the two-dimensional inverse scattering problem for a sound-soft or perfectly conducting obstacle we may distinguish between uniqueness results on three different levels. Consider the scatteringExpand
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Variational formulation of problems involving fractional order differential operators
In this work, we consider boundary value problems involving either Caputo or Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1), which are investigated from a variational point of view. Expand
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An inverse problem for a one-dimensional time-fractional diffusion problem
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed timeExpand
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A tutorial on inverse problems for anomalous diffusion processes
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopicExpand
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The determination of a discontinuity in a conductivity from a single boundary measurement
We consider the determination of the interior domain where D is characterized by a different conductivity from the surrounding medium. This amounts to solving the inverse problem of recovering theExpand
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The recovery of potentials from finite spectral data
The reconstruction of a Sturm–Liouville potential from finite spectral data is considered. A numerical technique based on a shooting method determines a potential with the given spectral data.Expand
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