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Approximation orders of and
"... approximation maps from local principal shiftinvariant spaces ..."
Approximation orders of FSI spaces in ...
, 1996
"... A second look at the authors' ([BDR1], [BDR2]) characterization of the approximation order of a Finitely generated ShiftInvariant subspace S(#) of L 2 (IR )results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators # # of the subspace. Further, ..."
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Cited by 24 (6 self)
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A second look at the authors' ([BDR1], [BDR2]) characterization of the approximation order of a Finitely generated ShiftInvariant subspace S(#) of L 2 (IR )results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators # # of the subspace. Further
Approximation Order of Tempered Distributions
, 2005
"... Properties of projections hj of a tempered distribution h to the corresponding spaces Vj, j ∈ Z, in a regular multiresolution approximation of L 2 (R) are studied. It is shown that the derivatives of hj multiplied by a polynomial weight converge in sup norm, i.e. hj → h in Sr(R), h being smooth enou ..."
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enough and of appropriate decay. Results related to tempered distributions are obtained by duality. The analysis of the approximation order of the projection operator within the framework of the theory of shiftinvariant spaces gives a further refinement of the results. As an application, we give Abelian
Approximate Signal Processing
, 1997
"... It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tra ..."
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Cited by 516 (2 self)
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these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a
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 874 (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
The space complexity of approximating the frequency moments
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1996
"... The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, ..."
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Cited by 855 (12 self)
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The frequency moments of a sequence containing mi elements of type i, for 1 ≤ i ≤ n, are the numbers Fk = �n i=1 mki. We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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hard. We prove that (1 \Gamma o(1)) ln n is a threshold below which set cover cannot be approximated efficiently, unless NP has slightly superpolynomial time algorithms. This closes the gap (up to low order terms) between the ratio of approximation achievable by the greedy algorithm (which is (1 \Gamma
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
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Cited by 959 (2 self)
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are worth striving for. It is shown that these features can be obtained by constructing a matrix with a certain “Property U.” Matrices having this property are exhibited for the equations of steady and unsteady gasdynamics. In order to construct them, it is found helpful to introduce “parameter vectors
Results 1  10
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