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Second Order Numerical Methods for. . .
, 1999
"... 3.54> 9:67 e \Gamma 04 1:0 2:27 e \Gamma 03 1:0 2nd Order I 21 14 1:51 e \Gamma 01 \Gamma 2:23 e \Gamma 01 \Gamma 2:61 e \Gamma 02 \Gamma 7:47 e \Gamma 02 \Gamma 41 14 4:92 e \Gamma 02 1:6 1:37 e \Gamma 01 0:7 2:59 e \Gamma 03 3:3 1:08 e \Gamma 02 2:8 81 14 1:44 e \Gamma 02 1:8 7:64 e \Gamma 02 ..."
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3.54> 9:67 e \Gamma 04 1:0 2:27 e \Gamma 03 1:0 2nd Order I 21 14 1:51 e \Gamma 01 \Gamma 2:23 e \Gamma 01 \Gamma 2:61 e \Gamma 02 \Gamma 7:47 e \Gamma 02 \Gamma 41 14 4:92 e \Gamma 02 1:6 1:37 e \Gamma 01 0:7 2:59 e \Gamma 03 3:3 1:08 e \Gamma 02 2:8 81 14 1:44 e \Gamma 02 1:8 7:64 e \Gamma 02
ON A UNIFORMLY SECOND ORDER NUMERICAL METHOD FOR THE ONEDIMENSIONAL DISCRETEORDINATE TRANSPORT EQUATION AND ITS DIFFUSION LIMIT WITH INTERFACE ∗
"... Abstract. In this paper, we study a uniformly second order numerical method for the discreteordinate transport equation in the slab geometry in the diffusive regimes with interfaces. At the interfaces, the scattering coefficients have discontinuities, so suitable interface conditions are needed to d ..."
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Cited by 3 (2 self)
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Abstract. In this paper, we study a uniformly second order numerical method for the discreteordinate transport equation in the slab geometry in the diffusive regimes with interfaces. At the interfaces, the scattering coefficients have discontinuities, so suitable interface conditions are needed
Unified analysis of discontinuous Galerkin methods for elliptic problems
 SIAM J. Numer. Anal
, 2001
"... Abstract. We provide a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment ..."
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Cited by 523 (31 self)
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Abstract. We provide a framework for the analysis of a large class of discontinuous methods for secondorder elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical
Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition
, 1998
"... Abstract. This paper is a survey of the inverse scattering problem for timeharmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering ” and Newtontype methods for solving the inverse scattering problem for acoustic waves, including a brief discussi ..."
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Cited by 1061 (45 self)
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discussion of Tikhonov’s method for the numerical solution of illposed problems. We then proceed to prove a uniqueness theorem for the inverse obstacle problems for acoustic waves and the linear sampling method for reconstructing the shape of a scattering obstacle from far field data. Included in our
Numerical Solutions of the Euler Equations by Finite Volume Methods Using RungeKutta TimeStepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 509 (78 self)
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A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used
The RungeKutta discontinuous Galerkin method for conservation laws V: multidimensional systems
, 1997
"... This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are describ ..."
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Cited by 508 (43 self)
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This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 536 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting
Approximating discrete probability distributions with dependence trees
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1968
"... A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n variables ..."
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Cited by 878 (0 self)
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A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n
Nonlinear total variation based noise removal algorithms
, 1992
"... A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the g ..."
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Cited by 2279 (51 self)
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the gradientprojection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t ~ 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear
A review of image denoising algorithms, with a new one
 SIMUL
, 2005
"... The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding perf ..."
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Cited by 509 (6 self)
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and, second, to propose a nonlocal means (NLmeans) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise, ” defined as the difference between a digital image and its denoised version. The NLmeans algorithm
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