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Average best mterm approximation
, 2010
"... We introduce the concept of average best mterm approximation widths with respect to a probability measure on the unit ball of ℓn p. We estimate these quantities for the embedding id: ℓn p → ℓn q with 0 < p ≤ q ≤ ∞ for the normalized cone and surface measure. Furthermore, we consider certain ten ..."
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Cited by 1 (0 self)
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We introduce the concept of average best mterm approximation widths with respect to a probability measure on the unit ball of ℓn p. We estimate these quantities for the embedding id: ℓn p → ℓn q with 0 < p ≤ q ≤ ∞ for the normalized cone and surface measure. Furthermore, we consider certain
The best mterm approximation and greedy algorithms
 Adv. Comput. Math
, 1998
"... Abstract. We study nonlinear mterm approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f ∈ H and any dictionary D an expansion into a series f = cj(f)ϕj(f), ϕj(f) ∈ ..."
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Abstract. We study nonlinear mterm approximation with regard to a redundant dictionary D in a Hilbert space H. It is known that the Pure Greedy Algorithm (or, more generally, the Weak Greedy Algorithm) provides for each f ∈ H and any dictionary D an expansion into a series f = cj(f)ϕj(f), ϕj
Best mTerm Approximation and SobolevBesov Spaces of Dominating Mixed Smoothness  the Case of Compact Embeddings
, 2010
"... ..."
Curvelets: a surprisingly effective nonadaptive representation of objects with edges
 IN CURVE AND SURFACE FITTING: SAINTMALO
, 2000
"... It is widely believed that to efficiently represent an otherwise smooth object with discontinuities along edges, one must use an adaptive representation that in some sense ‘tracks ’ the shape of the discontinuity set. This folkbelief — some would say folktheorem — is incorrect. At the very least ..."
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Cited by 395 (21 self)
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. By applying naive thresholding to the curvelet transform of such an object, one can form mterm approximations with rate of L 2 approximation rivaling the rate obtainable by complex adaptive schemes which attempt to ‘track ’ the discontinuity set. In this article we explain the basic issues of efficient mterm
An extrapolation theorem for nonlinear approximation and its applications ଁ
, 2006
"... Abstract We prove an extrapolation theorem for the nonlinear mterm approximation with respect to a system of functions satisfying very mild conditions. This theorem allows us to prove endpoint L p − L q estimates in nonlinear approximation. As a consequence, some known endpoint estimates can be de ..."
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Abstract We prove an extrapolation theorem for the nonlinear mterm approximation with respect to a system of functions satisfying very mild conditions. This theorem allows us to prove endpoint L p − L q estimates in nonlinear approximation. As a consequence, some known endpoint estimates can
The Concept of a Linguistic Variable and its Application to Approximate Reasoning
 Journal of Information Science
, 1975
"... By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young, et ..."
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Cited by 1430 (9 self)
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, etc., rather than 20, 21, 22, 23, In more specific terms, a linguistic variable is characterized by a quintuple (&?, T(z), U, G,M) in which &? is the name of the variable; T(s) is the termset of2, that is, the collection of its linguistic values; U is a universe of discourse; G is a syntactic
Some remarks on nonlinear approximation with Schauder bases
 East J. Approx
"... We study the approximation classes As and Gs associated with nonlinear mterm approximation and greedy approximation by elements from a quasinormed Schauder basis in a separable Banach space. We show that there always is a twosided embedding ..."
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Cited by 20 (3 self)
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We study the approximation classes As and Gs associated with nonlinear mterm approximation and greedy approximation by elements from a quasinormed Schauder basis in a separable Banach space. We show that there always is a twosided embedding
Results 1  10
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