Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems
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DOI: 10.1007/s10208-021-09536-6
Abstract: Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and… read more here.
Keywords: ill posed; convergence rates; posed problems; linear ill ... See more keywords
Solution methods for linear discrete ill-posed problems for color image restoration
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DOI: 10.1007/s10543-018-0706-0
Abstract: This work discusses four algorithms for the solution of linear discrete ill-posed problems with several right-hand side vectors. These algorithms can be applied, for instance, to multi-channel image restoration when the image degradation model is… read more here.
Keywords: image; linear discrete; ill posed; posed problems ... See more keywords
An iterative method to compute minimum norm solutions of ill-posed problems in Hilbert spaces
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DOI: 10.1007/s13370-019-00685-0
Abstract: We study an algorithm to compute minimum norm solution of ill-posed problems in Hilbert spaces and investigate its regularizing properties with discrepancy principle stopping rule. This algorithm results from straightly applying the LSQR method to… read more here.
Keywords: compute minimum; minimum norm; ill posed; method ... See more keywords
Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations
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DOI: 10.1088/1361-6420/ab9c45
Abstract: 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 $A^TAx=A^Tb$,… read more here.
Keywords: linear discrete; rank approximations; ill posed; discrete ill ... See more keywords
Iterative Fejér Processes in Ill-Posed Problems
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DOI: 10.1134/s0965542520060111
Abstract: A brief survey is given concerning iterative processes of Fejer type for basic statements of ill-posed problems, including constrained quadratic and convex minimization problems, variational inequalities, and linear and nonlinear operator equations in Hilbert spaces.… read more here.
Keywords: ill posed; processes ill; posed problems; fej processes ... See more keywords