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The Lavrentievregularized Galerkin method for linear accretive illposed problems
"... In this paper, for the numerical solution of linear accretive illposed problems in Hilbert spaces, Lavrentiev's mtimes iterated method is applied to the Galerkin equations, i.e., for each øxed discretization level the arising Galerkin equations are regularized by Lavrentiev's mtimes ite ..."
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In this paper, for the numerical solution of linear accretive illposed problems in Hilbert spaces, Lavrentiev's mtimes iterated method is applied to the Galerkin equations, i.e., for each øxed discretization level the arising Galerkin equations are regularized by Lavrentiev's m
Greedy Tikhonov regularization for large linear illposed problems
"... Several numerical methods for the solution of large linear illposed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov su ..."
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Cited by 2 (1 self)
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Several numerical methods for the solution of large linear illposed problems combine Tikhonov regularization with an iterative method based on partial Lanczos bidiagonalization of the operator. This paper discusses the determination of the regularization parameter and the dimension of the Krylov
Iterative Exponential Filtering for Large Discrete IllPosed Problems
"... We describe a new iterative method for the solution of large, very illconditioned linear systems of equations that arise when discretizing linear illposed problems. The righthand side vector represents the given data and is assumed to be contaminated by measurement errors. Our method applies a fi ..."
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Cited by 14 (7 self)
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We describe a new iterative method for the solution of large, very illconditioned linear systems of equations that arise when discretizing linear illposed problems. The righthand side vector represents the given data and is assumed to be contaminated by measurement errors. Our method applies a
Iterative Methods with Perturbations for IllPosed Problems
"... We consider regularizing iterative procedures for illposed problems with random and nonrandom additive errors. The rate of squaremean convergence for iterative procedures with random errors is studied. The comparison theorem is established for the convergence of procedures with and without additi ..."
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We consider regularizing iterative procedures for illposed problems with random and nonrandom additive errors. The rate of squaremean convergence for iterative procedures with random errors is studied. The comparison theorem is established for the convergence of procedures with and without
THE USE OF THE LCURVE IN THE REGULARIZATION OF DISCRETE ILLPOSED PROBLEMS*
"... Abstract. Regularization algorithms are often used to produce reasonable solutions to illposed problems. The Lcurve is a plotfor all valid regularization parametersof the size of the regularized solution versus the size of the corresponding residual. Two main results are established. First a u ..."
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Abstract. Regularization algorithms are often used to produce reasonable solutions to illposed problems. The Lcurve is a plotfor all valid regularization parametersof the size of the regularized solution versus the size of the corresponding residual. Two main results are established. First a
Lagrangian methods for the regularization of discrete illposed problems
"... In many science and engineering applications, the discretization of linear illposed problems gives rise to large illconditioned linear systems with righthand side degraded by noise. The solution of such linear systems requires the solution of a minimization problem with one quadratic constraint ..."
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In many science and engineering applications, the discretization of linear illposed problems gives rise to large illconditioned linear systems with righthand side degraded by noise. The solution of such linear systems requires the solution of a minimization problem with one quadratic constraint
ON THE ITERATIVELY REGULARIZED GAUSSNEWTON METHOD FOR SOLVING NONLINEAR ILLPOSED PROBLEMS
"... Abstract. The iteratively regularized GaussNewton method is applied to compute the stable solutions to nonlinear illposed problems F (x) =y when the data y is given approximately by yδ with ‖yδ − y ‖ ≤δ. In this method, the iterative sequence {xδ k} is defined successively by ..."
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Abstract. The iteratively regularized GaussNewton method is applied to compute the stable solutions to nonlinear illposed problems F (x) =y when the data y is given approximately by yδ with ‖yδ − y ‖ ≤δ. In this method, the iterative sequence {xδ k} is defined successively by
Optimal Regularization for IllPosed Problems in Metric Spaces
"... We present a strategy for choosing the regularization parameter (Lepskĳtype balancing principle) for illposed problems in metric spaces with deterministic or stochastic noise. Additionally we improve the strategy in comparison to the previously used version for Hilbert spaces in some ways. AMSCla ..."
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Cited by 3 (2 self)
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We present a strategy for choosing the regularization parameter (Lepskĳtype balancing principle) for illposed problems in metric spaces with deterministic or stochastic noise. Additionally we improve the strategy in comparison to the previously used version for Hilbert spaces in some ways. AMS
An Implicit Shift Bidiagonalization Algorithm For IllPosed Systems
 BIT
, 1994
"... . Iterative methods based on Lanczos bidiagonalization with full reorthogonalization (LBDR) are considered for solving large scale discrete illposed linear least squares problems of the form min x kAx \Gamma bk 2 . Methods for regularization in the Krylov subspaces are discussed which use generali ..."
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Cited by 22 (0 self)
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. Iterative methods based on Lanczos bidiagonalization with full reorthogonalization (LBDR) are considered for solving large scale discrete illposed linear least squares problems of the form min x kAx \Gamma bk 2 . Methods for regularization in the Krylov subspaces are discussed which use
An iterative multigrid regularization method for Toeplitz discrete illposed problems∗
"... Abstract. Iterative regularization multigrid methods have been successful applied to signal/image deblurring problems. When zeroDirichlet boundary conditions are imposed the deblurring matrix has a Toeplitz structure and it is potentially full. A crucial task of a multilevel strategy is to preserve ..."
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Abstract. Iterative regularization multigrid methods have been successful applied to signal/image deblurring problems. When zeroDirichlet boundary conditions are imposed the deblurring matrix has a Toeplitz structure and it is potentially full. A crucial task of a multilevel strategy
Results 11  20
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1,016