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Weak solutions to a nonlinear variational wave equation with general data
 Annals of Inst. H. Poincaré
"... We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values. ..."
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Cited by 17 (9 self)
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We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values.
Global Conservative Solutions to a Nonlinear Variational Wave Equation
, 2008
"... We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values. ..."
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Cited by 1 (0 self)
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We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0, for initial data of finite energy. Here c(·) is any smooth function with uniformly positive bounded values.
GLOBAL SEMIGROUP OF CONSERVATIVE SOLUTIONS OF THE NONLINEAR VARIATIONAL WAVE EQUATION
"... Abstract. We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0. We allow for initial data ut=0 and utt=0 that contain measures. We assume that 0 < κ −1 ≤ c(u) ≤ κ. Solutions of this equation may experience con ..."
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Cited by 6 (0 self)
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Abstract. We prove the existence of a global semigroup for conservative solutions of the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0. We allow for initial data ut=0 and utt=0 that contain measures. We assume that 0 < κ −1 ≤ c(u) ≤ κ. Solutions of this equation may experience
A CONVERGENT FINITE DIFFERENCE METHOD FOR A NONLINEAR VARIATIONAL WAVE EQUATION
"... Abstract. We establish rigorously convergence of a semidiscrete upwind scheme for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0 with ut=0 = u0 and utt=0 = v0. Introducing Riemann invariants R = ut + cux and S = ut − cux, the variational wave equation is equivalent to Rt − cRx = ..."
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Abstract. We establish rigorously convergence of a semidiscrete upwind scheme for the nonlinear variational wave equation utt − c(u)(c(u)ux)x = 0 with ut=0 = u0 and utt=0 = v0. Introducing Riemann invariants R = ut + cux and S = ut − cux, the variational wave equation is equivalent to Rt − c
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 2270 (52 self)
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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
An introduction to variational methods for graphical models
 TO APPEAR: M. I. JORDAN, (ED.), LEARNING IN GRAPHICAL MODELS
"... ..."
A New Extension of the Kalman Filter to Nonlinear Systems
, 1997
"... The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which ..."
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Cited by 747 (6 self)
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The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
Results 1  10
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708,577