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Lcurves and discrete illposed problems
 BIT
"... The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. This paper discusses application of the GMRES method to the solution of large linear systems of equations that arise from the discretization of linear illpose ..."
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Cited by 11 (8 self)
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problems. These linear systems are severely illconditioned and are referred to as discrete illposed problems. We are concerned with the situation when the righthand side vector is contaminated by measurement errors, and we discuss how a meaningful approximate solution of the discrete illposed problem
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
Illposed problems in early vision
 Proceedings of the IEEE
, 1988
"... The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detect ..."
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Cited by 226 (14 self)
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detection. These are inverse problems, which are often illposed or illconditioned. We review here the relevant mathematical results on illposed and illconditioned problems and introduce the formal aspects of regularization theory in the linear and nonlinear case. Specific topics in early vision
Regularization tools – a matlab package for analysis and solution of discrete illposed problems
 Numerical Algorithms
, 1994
"... The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents ..."
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Cited by 276 (8 self)
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The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents
An Lcurve for the MINRES method
"... A variant of the MINRES method, often referred to as the MRII method, has in the last few years become a popular iterative scheme for computing approximate solutions of large linear discrete illposed problems with a symmetric matrix. It is important to terminate the iterations sufficiently early i ..."
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Cited by 6 (3 self)
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A variant of the MINRES method, often referred to as the MRII method, has in the last few years become a popular iterative scheme for computing approximate solutions of large linear discrete illposed problems with a symmetric matrix. It is important to terminate the iterations sufficiently early
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
Mean shift, mode seeking, and clustering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... AbstractMean shift, a simple iterative procedure that shifts each data point to the average of data points in its neighborhood, is generalized and analyzed in this paper. This generalization makes some kmeans like clustering algorithms its special cases. It is shown that mean shift is a modeseeki ..."
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Cited by 620 (0 self)
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seeking process on a surface constructed with a “shadow ” kernel. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis is treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications
Rules, discretion, and reputation in a model of monetary policy
 JOURNAL OF MONETARY ECONOMICS
, 1983
"... In a discretionary regime the monetary authority can print more money and create more inflation than people expect. But, although these inflation surprises can have some benefits, they cannot arise systematically in equilibrium when people understand the policymakor's incentives and form their ..."
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Cited by 794 (9 self)
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the policymaker and the private agents, it is possible that reputational forces can substitute for formal rules. Here, we develop an example of a reputational equilibrium where the outcomes turn out to be weighted averages of those from discretion and those from the ideal rule. In particular, the rates
REGULARIZATION PARAMETER DETERMINATION FOR DISCRETE ILLPOSED PROBLEMS∗
"... Abstract. Straightforward solution of discrete illposed linear systems of equations or leastsquares problems with error contaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. The problems have to be modified to reduce their sensiti ..."
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Abstract. Straightforward solution of discrete illposed linear systems of equations or leastsquares problems with error contaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. The problems have to be modified to reduce
LanczosBased Exponential Filtering for Discrete IllPosed Problems
, 2002
"... We describe regularizing iterative methods for the solution of large illconditioned linear systems of equations that arise from the discretization of linear illposed problems. The regularization is specified by a filter function of Gaussian type. A parameter determines the amount of regularization ..."
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Cited by 13 (5 self)
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We describe regularizing iterative methods for the solution of large illconditioned linear systems of equations that arise from the discretization of linear illposed problems. The regularization is specified by a filter function of Gaussian type. A parameter determines the amount
Results 1  10
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1,377,729