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19,963
Approximation error for quasiinterpolators and (multi)wavelet expansions
 APPL. COMPUT. HARMON. ANAL
, 1999
"... We investigate the approximation properties of general polynomial preserving operators that approximate a function into some scaled subspace of L² via an appropriate sequence of inner products. In particular, we consider integer shiftinvariant approximations such as those provided by splines and wa ..."
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Cited by 64 (22 self)
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and wavelets, as well as finite elements and multiwavelets which use multiple generators. We estimate the approximation error as a function of the scale parameter T when the function to approximate is sufficiently regular. We then present a generalized sampling theorem, a result that is rich enough to provide
Approximate Statistical Tests for Comparing Supervised Classification Learning Algorithms
, 1998
"... This article reviews five approximate statistical tests for determining whether one learning algorithm outperforms another on a particular learning task. These tests are compared experimentally to determine their probability of incorrectly detecting a difference when no difference exists (type I err ..."
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Cited by 723 (8 self)
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This article reviews five approximate statistical tests for determining whether one learning algorithm outperforms another on a particular learning task. These tests are compared experimentally to determine their probability of incorrectly detecting a difference when no difference exists (type I
Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
 in Conference Record of The TwentySeventh Asilomar Conference on Signals, Systems and Computers
, 1993
"... In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang (199 ..."
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Cited by 637 (1 self)
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recursively. where fk is the current approximation, and Rkf the current residual (error). Using initial values ofR0f = 1, fo = 0, and k = 1, the MP algorithm is comprised of the following steps,.,.41) Compute the innerproducts {(Rkf,z)}. (H) Find flki such that (III) Set, I(R*f,1:n 1+,)l asupl
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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to work well. In this paper we investigate loopy prop agation empirically under a wider range of conditions. Is there something special about the errorcorrecting code setting, or does loopy propagation work as an approximation scheme for a wider range of networks? ..\ x(:x).) (1) where: and: The message
1 Exact and Approximated error of the FMA
, 2009
"... The fused multiply accumulateadd (FMA) instruction, specified by the IEEE 7542008 Standard for FloatingPoint Arithmetic, eases some calculations, and is already available on some current processors such as the Power PC or the Itanium. We first extend an earlier work on the computation of the exac ..."
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of the exact error of an FMA (by giving more general conditions and providing a formal proof). Then, we present a new algorithm that computes an approximation to the error of an FMA, and provide error bounds and a formal proof for that algorithm.
ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION
"... Mathematical models are often described by multivariate functions, which are usually approximated by a sum of lower dimensional functions. A major problem is the approximation error introduced and the factors that affect it. This paper investigates the error of approximating a multivariate function ..."
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Mathematical models are often described by multivariate functions, which are usually approximated by a sum of lower dimensional functions. A major problem is the approximation error introduced and the factors that affect it. This paper investigates the error of approximating a multivariate function
Bounds of the Expected Approximation Error in Optimal Inventory Policies
"... Bounds for the approximation error of optimal inventory policies are derived. The unknown distribution functions are approximated by normal distributions. The expectation of the errors are of order 0[log(N) 1 2 ]: 1 Introduction The present trend towards the introduction of new techniques in the ..."
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Bounds for the approximation error of optimal inventory policies are derived. The unknown distribution functions are approximated by normal distributions. The expectation of the errors are of order 0[log(N) 1 2 ]: 1 Introduction The present trend towards the introduction of new techniques
Results 11  20
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19,963