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On pΛbounded variation
 Bull. Iranian Math. Soc
"... Abstract. A characteriation of continuity of the pΛvariation function is given and the Helly’s selection principle for ΛBV (p) functions is established. A characterization of the inclusion of WatermanShiba classes into classes of functions with given integral modulus of continuity is given. A us ..."
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Cited by 3 (3 self)
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Abstract. A characteriation of continuity of the pΛvariation function is given and the Helly’s selection principle for ΛBV (p) functions is established. A characterization of the inclusion of WatermanShiba classes into classes of functions with given integral modulus of continuity is given. A
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
Floating drops and functions of bounded variation
, 2007
"... A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been st ..."
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Cited by 1 (0 self)
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A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been
PROPERTIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION
"... Abstract. The class of functions of ΛBV (p) shares many properties of functions of bounded variation. Here we have shown that ΛBV (p) is a Banach space with a suitable norm, the intersection of ΛBV (p), over all sequences Λ, is the class of functions of BV(p) and the union of ΛBV (p), over all sequ ..."
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Cited by 4 (0 self)
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Abstract. The class of functions of ΛBV (p) shares many properties of functions of bounded variation. Here we have shown that ΛBV (p) is a Banach space with a suitable norm, the intersection of ΛBV (p), over all sequences Λ, is the class of functions of BV(p) and the union of ΛBV (p), over all
ON POINCARÉWIRTINGER INEQUALITIES IN SPACES OF FUNCTIONS OF BOUNDED VARIATION
"... Abstract. The goal of this paper is to extend PoincaréWirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order. ..."
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Abstract. The goal of this paper is to extend PoincaréWirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order.
The sharp quantitative Sobolev inequality for functions of bounded variation
 J. Funct. Anal
"... Abstract. The classical Sobolev embedding theorem of the space of functions of bounded variation BV (Rn) into Ln ′ (Rn) is proved in a sharp quantitative form. 1. ..."
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Cited by 13 (4 self)
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Abstract. The classical Sobolev embedding theorem of the space of functions of bounded variation BV (Rn) into Ln ′ (Rn) is proved in a sharp quantitative form. 1.
Divergence measures based on the Shannon entropy
 IEEE Transactions on Information theory
, 1991
"... AbstractA new class of informationtheoretic divergence measures based on the Shannon entropy is introduced. Unlike the wellknown Kullback divergences, the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved. More importantly, ..."
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Cited by 666 (0 self)
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, their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds. These bounds are crucial in many applications of divergence measures. The new measures are also well characterized by the properties of nonnegativity, finiteness
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Variational algorithms for approximate Bayesian inference
, 2003
"... The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents ..."
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Cited by 440 (9 self)
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a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propagation algorithms. Chapter 2 forms
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 907 (36 self)
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the variation in the perturbed quantity. Up to the higherorder terms that are ignored in the expansion, these statistics tend to be more realistic than perturbation bounds obtained in terms of norms. The technique is applied to a number of problems in matrix perturbation theory, including least squares
Results 1  10
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5,939