Search Results - Ill-posedness and regularization problems in numerical linear algebra

Flipped structured matrix-sequences in image deblurring with reflective and anti-reflective boundary conditions by Ferrari, Paola, Furci, Isabella, Serra-Capizzano, Stefano

“…Motivated by the recent work (Donatelli et al. Electron. Trans. Numer. Anal. 59 , 157-178 2023) on a preconditioned MINRES for flipped linear systems in imaging with Dirichlet boundary conditions…”
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Large-scale Tikhonov regularization via reduction by orthogonal projection by Lampe, Jörg, Reichel, Lothar, Voss, Heinrich

“…This paper presents a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed least-squares problems with a general regularization matrix…”
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Local linear convergence of approximate projections onto regularized sets by Luke, D. Russell

“…The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection…”
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A modified method for a backward heat conduction problem by Qian, Zhi, Fu, Chu-Li, Shi, Rui

“…We consider a backward heat conduction problem in a strip, where data is given at the final time t = T( T…”
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Efficient Algorithms for Solution of Regularized Total Least Squares by Renaut, Rosemary A., Guo, Hongbin

“… [SIAM J. Matrix Anal. Appl., 21 (1999), pp. 185--194] presented a parameter-dependent direct algorithm for the solution of the augmented Lagrange formulation for the RTLS problem, and Sima, Van Huffel, and Golub…”
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COMPUTATION OF FOURIER TRANSFORMS FOR NOISY BANDLIMITED SIGNALS by CHEN, WEIDONG

“…In this paper, the ill-posed problem of computation of the Fourier transform $\hat f$ for a noisy bandlimited signal f is discussed…”
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Approximate Diagonalization by Davies, E. B.

“… We formulate a conjecture about its efficiency and provide both theoretical and numerical evidence in support of the conjecture…”
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On the well-posedness for Keller-Segel system with fractional diffusion by Wu, Gang, Zheng, Xiaoxin

“…–Paley theory, we get a local well‐posedness result and a global well‐posedness result with a small initial data. In addition, ill‐posedness for ‘doubly parabolic…”
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A numerical method for solving the Dirichlet problem for the wave equation by Kabanikhin, S. I., Krivorot’ko, O. I.

“… We analyze the ill-posedness of the problem and construct a regularization algorithm. Using the Fourier series expansion with respect to one variable, we reduce the problem to a sequence of Dirichlet problems for one-dimensional wave equations…”
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A Unifying Representer Theorem for Inverse Problems and Machine Learning by Unser, Michael

“…Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements…”
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Comparison of four natural pixel bases for SPECT imaging by Bevilacqua, R., Bozzo, E., Menchi, O.

“…In this paper the problem of restoring a two-dimensional tomographic medical image is considered…”
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Constructing the physical parameters of a damped vibrating system from eigendata by Bai, Zheng-Jian

“…In this paper we consider the inverse problem for a discrete damped mass–spring system where the mass, damping, and stiffness matrices are all symmetric tridiagonal…”
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Generalized Tikhonov-type regularization method for the Cauchy problem of a semi-linear elliptic equation by Zhang, Hongwu, Zhang, Xiaoju

“…This paper considers the Cauchy problem of a semi-linear elliptic equation and uses a generalized Tikhonov-type regularization method to overcome its ill-posedness…”
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Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation by Sun, Yao

“… The ill-posedness is dealt with Tikhonov regularization, whilst the optimal regularization parameter is chosen by Morozov discrepancy principle…”
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A new wavelet method for solving an ill-posed problem by Qian, Ailin

“… Due to ill-posedness of this problem, we provide a regularization method – wavelet dual least squares method to solve the problem…”
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A regularization of nonlinear diffusion equations in a multiresolution framework by Teschke, Gerd, Zhariy, Mariya, Soares, Maria Joana

“… The main result of this paper is to show that the chosen discretization overcomes the ill posedness of the nonlinear Perona–Malik model…”
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A Fast Method for Finding the Global Solution of the Regularized Structured Total Least Squares Problem for Image Deblurring by Beck, Amir, Ben-Tal, Aharon, Kanzow, Christian

“… To avoid ill posedness, a regularization term is added to the objective function; this leads to the so-called regularized TLS problem…”
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A stabilized multigrid solver for hyperelastic image registration by Ruthotto, Lars, Greif, Chen, Modersitzki, Jan

“… To ensure that numerical solutions satisfy this requirement, we discretize the variational problem using piecewise linear finite elements, and then solve the discrete optimization problem using the Gauss–Newton method…”
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Computation of the inverse Laplace transform based on a collocation method which uses only real values by Cuomo, S., D’Amore, L., Murli, A., Rizzardi, M.

“… Difficulties associated with these problems are due to their intrinsic ill-posedness. The main contribution of this paper is to provide computable estimates of truncation…”
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The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data by HNETYNKOVA, Iveta, PLESINGER, Martin, STRAKOS, Zdenek

“… The projected problem, however, inherits a part of the ill-posedness of the original problem, and therefore some form of inner regularization must be applied…”
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