A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime [PDF]
, 2019 The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit dependence on ...
Burman, Erik +2 more
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Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve
International Journal of Applied Mathematics and Computer Sciences, 2007 Regularization Parameter Selection in Discrete Ill-Posed Problems — The Use of the U-Curve To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used.
D. Krawczyk-Stando, M. Rudnicki
semanticscholar +1 more source
Embedded techniques for choosing the parameter in Tikhonov regularization
, 2013 This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method.
Gazzola, Silvia +2 more
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An asymptotic preserving scheme for strongly anisotropic elliptic problems [PDF]
, 2009 In this article we introduce an asymptotic preserving scheme designed to compute the solution of a two dimensional elliptic equation presenting large anisotropies.
Degond, Pierre +2 more
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Decomposition methods for large linear discrete ill-posed problems
Journal of Computational and Applied Mathematics, 2007 The authors present decomposition methods for large linear discrete ill-posed problems. The main idea is a splitting of the solution space into a Krylov subspace determined by a standard iterative method of GMRES-type or the least squares QR method and a user-supplied subspace.
Baglama, James, Reichel, Lothar
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Stabilized nonconforming finite element methods for data assimilation in incompressible flows [PDF]
, 2016 We consider a stabilized nonconforming finite element method for data assimilation in incompressible flow subject to the Stokes' equations. The method uses a primal dual structure that allows for the inclusion of nonstandard data.
Burman, Erik, Hansbo, Peter
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Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems [PDF]
Signal Processing, 2016 Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution.
M. Suliman, Tarig Ballal, T. Al-Naffouri
semanticscholar +1 more source
European Physical Journal C: Particles and FieldsWe systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard’s well-posedness criteria, existence and uniqueness of ...
Ao-Sheng Xiong +6 more
doaj +1 more source
Combining approximate solutions for linear discrete ill-posed problems
Journal of Computational and Applied Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hochstenbach, M.E., Reichel, L.
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Vector extrapolation enhanced TSVD for linear discrete ill-posed problems [PDF]
Numerical Algorithms, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jbilou, K., Reichel, L., Sadok, H.
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