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968
Gruenhage compacta and strictly convex dual norms
 J. Math. Anal. Appl
"... Abstract. We prove that if K is a Gruenhage compact space then C(K) ∗ admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X ∗ = span ·(K), where K is a Gruenhage compact in the w∗topology and   ·   is equivalent to a coarser, w∗low ..."
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Cited by 9 (5 self)
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Abstract. We prove that if K is a Gruenhage compact space then C(K) ∗ admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X ∗ = span ·(K), where K is a Gruenhage compact in the w∗topology and   ·   is equivalent to a coarser, w
The Steiner ratio for the dual normed plane
, 1997
"... A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimal possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of ..."
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Cited by 1 (0 self)
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of points in the metric space. Du et al. (1993) conjectured that the Steiner ratio on a normed plane is equal to the Steiner ratio on its dual plane. In this paper we show that this conjecture is true for Ixl ~<5.
◮ Energy norm ◮ Dual norm ◮ Error norm
"... ∂tu − div(d∇u) + a · ∇u + ru = f in Ω × (0, T] u = 0 on Γ × (0, T] u = u0 in Ω ◮ d> 0 ◮ r ≥ 0 ◮ a ∈ C1 (Ω × (0, T]) d ◮ div a = 0 in Ω × (0, T] ◮ a = 0 on Γ × (0, T] ..."
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∂tu − div(d∇u) + a · ∇u + ru = f in Ω × (0, T] u = 0 on Γ × (0, T] u = u0 in Ω ◮ d> 0 ◮ r ≥ 0 ◮ a ∈ C1 (Ω × (0, T]) d ◮ div a = 0 in Ω × (0, T] ◮ a = 0 on Γ × (0, T]
Smoothing Directional Vector Fields Using Dual Norms
, 2009
"... This paper provides a new variational paradigm to measure the smoothness of unit vector fields on spatial domains, leading to new methods for smoothing and interpolating such datasets. Our point of view is to consider unit vector fields as linear forms acting on reproducing kernel Hilbert spaces of ..."
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of vector fields or tensors and work with the dual norm, leading to new variational problems and algorithms. We prove, in particular, that these variational problems are wellposed, in the sense that optimal solutions exist in the space of unit vector fields. Experimental results are based on synthetic data
On the Use of Dual Norms in Bounded Variation Type Regularization
 Weickert (Eds.), Geometric Properties of Incomplete Data, in: Computational Imaging and Vision
, 2004
"... Recently Y. Meyer gave a characterization of the minimizer of the RudinOsherFatemi functional in terms of the Gnorm. In this work we generalize this result to regularization models with higher order derivatives of bounded variation. This requires us to define generalized Gnorms. We present some ..."
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Cited by 9 (1 self)
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Recently Y. Meyer gave a characterization of the minimizer of the RudinOsherFatemi functional in terms of the Gnorm. In this work we generalize this result to regularization models with higher order derivatives of bounded variation. This requires us to define generalized Gnorms. We present some
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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the smallest l 1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP and BOB, including better sparsity, and superresolution. BP has interesting relations to ideas in areas as diverse as illposed problems, in abstract harmonic analysis, total
Benchmarking Least Squares Support Vector Machine Classifiers
 NEURAL PROCESSING LETTERS
, 2001
"... In Support Vector Machines (SVMs), the solution of the classification problem is characterized by a (convex) quadratic programming (QP) problem. In a modified version of SVMs, called Least Squares SVM classifiers (LSSVMs), a least squares cost function is proposed so as to obtain a linear set of eq ..."
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Cited by 476 (46 self)
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of equations in the dual space. While the SVM classifier has a large margin interpretation, the LSSVM formulation is related in this paper to a ridge regression approach for classification with binary targets and to Fisher's linear discriminant analysis in the feature space. Multiclass categorization
Recovery of ScalarDiffusion From the Distributed Observation By Minimizing the Dual Norm
, 1996
"... The identification problem to recover the diffusion coefficient in a general elliptic equation is considered. For this purpose a method being a variant of the socalled equation error approach is suggested. A stability estimate for the method is given and, especially, very fast numerical algorithm ..."
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The identification problem to recover the diffusion coefficient in a general elliptic equation is considered. For this purpose a method being a variant of the socalled equation error approach is suggested. A stability estimate for the method is given and, especially, very fast numerical algorithm to solve the finite dimensional problem presented together with some computational results. Key Words. identification of diffusion coefficient, strongly monotone operators AMS Subject Classification. 65N30 1 Introduction We consider the elliptic equation \Gammadiv (a(x) gradu(x)) + L(u(x)) = f(x) in\Omega ; a @u @n = g(x) on @\Omega ; (1.1) where\Omega ae R 2 is a bounded, simplyconnected domain with Lipschitz boundary @\Omega : We assume that (1.1) defines a Lipschitz continuous and strongly monotone operator so that it has a unique solution u [28]. Equations like (1.1) can describe the behavior of many processes, e.g., in mechanics and biology [2]. For example, when L = 0 e...
Results 1  10
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968