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Choosing regularization parameters in iterative methods for illposed problems
 SIAM J. MATRIX ANAL. APPL
, 2001
"... Numerical solution of illposedproblems is often accomplishedby discretization (projection onto a finite dimensional subspace) followed by regularization. If the discrete problem has high dimension, though, typically we compute an approximate solution by projecting the discrete problem onto an even ..."
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Cited by 51 (6 self)
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an even smaller dimensional space, via iterative methods based on Krylov subspaces. In this work we present a common framework for efficient algorithms that regularize after this second projection rather than before it. We show that determining regularization parameters based on the final projectedproblem
A Compressive Landweber Iteration for Solving IllPosed Inverse Problems
, 2008
"... In this paper we shall be concerned with the construction of an adaptive Landweber iteration for solving linear illposed and inverse problems. Classical Landweber iteration schemes provide in combination with suitable regularization parameter rules order optimal regularization schemes. However, for ..."
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Cited by 124 (4 self)
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In this paper we shall be concerned with the construction of an adaptive Landweber iteration for solving linear illposed and inverse problems. Classical Landweber iteration schemes provide in combination with suitable regularization parameter rules order optimal regularization schemes. However
Pegasos: Primal Estimated subgradient solver for SVM
"... We describe and analyze a simple and effective stochastic subgradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a singl ..."
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Cited by 542 (20 self)
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single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ɛ2) iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total
Regularizing IllPosed Problems: Experiments With Multilevel Schemes
, 1994
"... . A brief survey of regularization algorithms and parameter selection procedures relevant to multilevel schemes is provided. A number of new multilevel algorithms for solving illposed problems is introduced. They include a multilevel Landweber iteration that resembles the TwomeyTikhonov scheme, and ..."
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Cited by 1 (0 self)
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. A brief survey of regularization algorithms and parameter selection procedures relevant to multilevel schemes is provided. A number of new multilevel algorithms for solving illposed problems is introduced. They include a multilevel Landweber iteration that resembles the TwomeyTikhonov scheme
An Iteratively Regularized Projection Method for Nonlinear Illposed Problems
"... An iterative regularization method in the setting of a finite dimensional subspace Xh of the real Hilbert space X has been considered for obtaining stable approximate solution to nonlinear illposed operator equations F (x) = y where F: D(F) ⊆ X − → X is a nonlinear monotone operator on X. We as ..."
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An iterative regularization method in the setting of a finite dimensional subspace Xh of the real Hilbert space X has been considered for obtaining stable approximate solution to nonlinear illposed operator equations F (x) = y where F: D(F) ⊆ X − → X is a nonlinear monotone operator on X. We
Analysis of Bounded Variation Penalty Methods for IllPosed Problems
 INVERSE PROBLEMS
, 1994
"... This paper presents an abstract analysis of bounded variation (BV) methods for illposed operator equations Au = z. Let T (u) def = kAu \Gamma zk 2 + ffJ(u); where the penalty, or "regularization", parameter ff ? 0 and the functional J(u) is the BV norm or seminorm of u, also known a ..."
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Cited by 171 (1 self)
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This paper presents an abstract analysis of bounded variation (BV) methods for illposed operator equations Au = z. Let T (u) def = kAu \Gamma zk 2 + ffJ(u); where the penalty, or "regularization", parameter ff ? 0 and the functional J(u) is the BV norm or seminorm of u, also known
REGULARIZATION PARAMETER SELECTION IN DISCRETE ILL–POSED PROBLEMS — THE USE OF THE U–CURVE
"... To obtain smooth solutions to illposed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the wellknown Lcurve criterion, based on the Lcurve which is a plot of the norm of the regularized soluti ..."
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Cited by 6 (0 self)
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To obtain smooth solutions to illposed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the wellknown Lcurve criterion, based on the Lcurve which is a plot of the norm of the regularized
Regularization of discrete illposed problems
, 2002
"... The paper concerns conditioning aspects of finite dimensional problems arisen when the Tikhonov regularization is applied to discrete illposed problems. A relation between a regularization parameter and sensitivity of regularized solution is investigated. Moreover, it is shown that choice of regula ..."
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The paper concerns conditioning aspects of finite dimensional problems arisen when the Tikhonov regularization is applied to discrete illposed problems. A relation between a regularization parameter and sensitivity of regularized solution is investigated. Moreover, it is shown that choice
Iterative Solution Methods for Large Linear Discrete IllPosed Problems
, 1998
"... This paper discusses iterative methods for the solution of very large severely illconditioned linear systems of equations that arise from the discretization of linear illposed problems. The righthand side vector represents the given data and is assumed to be contaminated by errors. Solution metho ..."
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Cited by 9 (5 self)
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This paper discusses iterative methods for the solution of very large severely illconditioned linear systems of equations that arise from the discretization of linear illposed problems. The righthand side vector represents the given data and is assumed to be contaminated by errors. Solution
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