Results 1 to 10 of about 319,161 (69)
Adaptive Spectral Inversion for inverse medium problems
Inverse Problems, 2023 Abstract A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based representations, the misfit is instead minimized in a small subspace spanned by the first few ...
Yannik G Gleichmann, Marcus J Grote
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Adaptive spectral decompositions for inverse medium problems [PDF]
Inverse Problems, 2021 Abstract Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to the high dimension of
Daniel H Baffet +2 more
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Inverse Spectral Problems in Rectangular Domains [PDF]
Communications in Partial Differential Equations, 2007 We consider the Schrodinger operator in n-dimensional rectangular domains with either Dirichlet or Neumann boundary conditions on the faces and study the constraints on the potential imposed by fixing the spectrum of the operator.We study also the asymptotics of the heat kernel when t tends to 0.
Eskin, Gregory, Ralston, James
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Inverse Steklov Spectral Problem for Curvilinear Polygons [PDF]
International Mathematics Research Notices, 2020 Abstract This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi $, we prove that the asymptotics of Steklov eigenvalues obtained in [ 20] determines, in a constructive manner, the number of vertices and the properly ordered sequence of side lengths, as
Krymski, S +4 more
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Integrable models for shallow water with energy dependent spectral problems [PDF]
, 2012 We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependance on the spectral parameter.
Ivanov, Rossen I., Lyons, Tony
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The inverse spectral problem for indefinite strings [PDF]
, 2014 Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form \[-u"=z\,u\,\omega+z^2u\,\upsilon\] on an
Eckhardt, Jonathan, Kostenko, Aleksey
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Well-posed inverse spectral problems [PDF]
Proceedings of the National Academy of Sciences, 1975 It is known that if complete spectral data are provided, the potential function in a Sturm-Liouville operator is uniquely determined almost everywhere. If two such operators have spectra that differ in a finite number of eigenvalues, then the corresponding potential functions will no longer be the same. However, as is demonstrated when the nonidentical
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Inverse Spectral Problems for Schrödinger Operators [PDF]
Communications in Mathematical Physics, 2009 In this article we improve some of the inverse spectral results proved by Guillemin and Uribe in \cite{GU}. They proved that under some symmetry assumptions on the potential $V(x)$, the Taylor expansion of $V(x)$ near a non-degenerate global minimum can be recovered from the knowledge of the low-lying eigenvalues of the associated Schr dinger operator
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Linear Algebra and its Applications, 1975 AbstractIn this article an infinite periodic Jacobi matrix is under consideration. It is shown that the spectrum of the matrix consists of a single finite interval if and only if the period of the matrix is equal to unity.
Cheung, Shiu Ming, Hochstadt, Harry
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Degasperis-Procesi peakons and the discrete cubic string [PDF]
, 2005 We use an inverse scattering approach to study multi-peakon solutions of the Degasperis-Procesi (DP) equation, an integrable PDE similar to the Camassa-Holm shallow water equation.
Lundmark, Hans, Szmigielski, Jacek
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