Results 21 to 30 of about 180,343 (197)
FGMRES for linear discrete ill-posed problems [PDF]
Applied Numerical Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Morikuni, Keiichi +2 more
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Square regularization matrices for large linear discrete ill‐posed problems [PDF]
Numerical Linear Algebra with Applications, 2012 SUMMARYLarge linear discrete ill‐posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods ...
DONATELLI, MARCO, Neuman A., Reichel L.
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Light: Science & Applications, 2021 Limited-angle tomography of an interior volume is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security.
Iksung Kang +2 more
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Inverse Problems, 2020 For the large-scale linear discrete ill-posed problem min‖Ax − b‖ or Ax = b with b contaminated by white noise, the Golub–Kahan bidiagonalization based LSQR method and its mathematically equivalent CGLS, the conjugate gradient (CG) method applied to ATAx
Zhongxiao Jia
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Projected Tikhonov Regularization of Large-Scale Discrete Ill-Posed Problems [PDF]
Journal of Scientific Computing, 2013 Least squares problems \(\min_{x \in \mathbb R^m} \| Ax - b \|\), \(A \in \mathbb R^{m \times n}\), \(b \in \mathbb R^m\) are considered where the singular values of \(A\) are clustered at the origin and the vector \(b\) is of the type \(b_{\text{true}} + e\) with a perturbation \(e \in \mathbb R^m\).
Martin, David R., Reichel, Lothar
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Regularizing Inverse Preconditioners for Symmetric Band Toeplitz Matrices
EURASIP Journal on Advances in Signal Processing, 2007 Image restoration is a widely studied discrete ill-posed problem. Among the many regularization methods used for treating the problem, iterative methods have been shown to be effective.
O. Menchi, G. Lotti, P. Favati
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Mathematical Modelling and Analysis, 2017 In the article the authors developed two efficient algorithms for solving severely ill-posed problems such as Fredholm’s integral equations. The standard Tikhonov method is applied as a regularization.
Sergii G. Solodky +2 more
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The structure of iterative methods for symmetric linear discrete ill-posed problems [PDF]
, 2014 The iterative solution of large linear discrete ill-posed problems with an error contaminated data vector requires the use of specially designed methods in order to avoid severe error propagation. Range restricted minimal residual methods have been found
A Neuman +21 more
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Generalized Cross-Validation applied to Conjugate Gradient for discrete ill-posed problems [PDF]
, 2014 To apply the Generalized Cross-Validation (GCV) as a stopping rule for an iterative method, we must estimate the trace of the so-called in?uence matrix which appears in the denominator of the GCV function.
Favati, Paola +3 more
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Multilevel Approach For Signal Restoration Problems With Toeplitz Matrices [PDF]
, 2010 We present a multilevel method for discrete ill-posed problems arising from the discretization of Fredholm integral equations of the first kind. In this method, we use the Haar wavelet transform to define restriction and prolongation operators within a ...
Español, Malena I., Kilmer, Misha E.
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