Robust Recovery of Optimally Smoothed Polymer Relaxation Spectrum from Stress Relaxation Test Measurements. [PDF]
Stankiewicz A.
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Optimizing quantitative photoacoustic imaging systems: the Bayesian Cramér-Rao bound approach. [PDF]
Scope Crafts E, Anastasio MA, Villa U.
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Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials. [PDF]
Stankiewicz A.
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Derivative-Free Iterative One-Step Reconstruction for Multispectral CT. [PDF]
Prohaszka T, Neumann L, Haltmeier M.
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VISTA-SSM: Varying and irregular sampling time-series analysis via state-space models. [PDF]
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A Regularization Parameter in Discrete Ill-Posed Problems
SIAM Journal on Scientific Computing, 1996The author considers the Tikhonov regularization method for the discrete ill-posed problem of minimizing \[ J_\alpha(u)=|Ku-f|^2+\alpha|u|^2, \] where \(K\) is an \(m\times n\) matrix with a large condition number, \(m\geq n\), and \(\alpha>0\). The Euclidean norm is used.
T. Reginska
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The discrete picard condition for discrete ill-posed problems
BIT, 1990For Fredholm integral equations of the first kind with nondegenerate kernels the Picard criterion simultaneously provides an existence criterion and elucidates the essential ill-posedness of the problem. The author develops a discrete Picard condition for the overdetermined ill- conditioned linear algebraic systems which arise from the discretization ...
P. Hansen
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GMRES, L-Curves, and Discrete Ill-Posed Problems
BIT Numerical Mathematics, 2002The application of the generalized minimal residual (GMRES) method is discussed for solving large systems of linear equations that arise from the discretization of linear ill-posed problems. The situation is considered when the right-hand side vector is contaminated by measurement errors.
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Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion
, 1987P. Hansen
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Numerical considerations of block GMRES methods when applied to linear discrete ill-posed problems
Journal of Computational and Applied Mathematics, 2023Linear systems of equations with a matrix whose singular values decay to zero with increasing index number without a significant gap are commonly referred to as linear discrete ill-posed problems.
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