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approximation errors
, 2010
"... For purposes of actual evaluation, mathematical functions f are commonly replaced by approximation polynomials p. Examples include floatingpoint implementations of elementary functions, quadrature or more theoretical proof work involving transcendental functions. Replacing f by p induces a relative ..."
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For purposes of actual evaluation, mathematical functions f are commonly replaced by approximation polynomials p. Examples include floatingpoint implementations of elementary functions, quadrature or more theoretical proof work involving transcendental functions. Replacing f by p induces a
Approximation Errors
, 2008
"... A bound on the error introduced by truncating a quantum addition is given. This bound shows that only a few controlled rotation gates will be necessary to get a reliable computation. ..."
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A bound on the error introduced by truncating a quantum addition is given. This bound shows that only a few controlled rotation gates will be necessary to get a reliable computation.
Approximation Error Maps
, 2001
"... Let F and A be two linear function spaces defined on some domain \Omega, and let * be a vector seminorm for the space A + F. We consider here the question of how well A approximates F in the sense of the metric *. Global error measures are insuficiently informative when the space A is not spati ..."
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Let F and A be two linear function spaces defined on some domain \Omega, and let * be a vector seminorm for the space A + F. We consider here the question of how well A approximates F in the sense of the metric *. Global error measures are insuficiently informative when the space A
Exact and Approximated Error of the FMA
, 2011
"... 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 exa ..."
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Cited by 1 (0 self)
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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.
COMPARISON OF THE APPROXIMATION ERRORS OF THE PREFILTERED
"... Abstract—We study the performance of the linear prediction (LP) method for blind channel identification when the true channel is of order, whereas the channel model is of order, with.By partitioning the true channel into the thorder significant part and the unmodeled tails, we show that the LP meth ..."
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the approximation performance of a special FIR prefilter. The results show that the convergent rate of the prefiltered projection is the same as that of the orthogonal projection. In addition, for bandlimited signals, the quantitative estimates of the upper bounds of the three types of errors are obtained
Sample Complexity versus Approximation Error
"... We consider the problem of learning an unknown realvalued function from a sequence of values of the function at randomly chosen points when the estimates are constrained to some class of functions called the hypothesis class. Ideally, thehypothesis class should be able to approximate a wide variety ..."
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variety of target functions, yet not need an excessive number of examples to ensure that a learning algorithm can choose a nearoptimal approximation to the target function. We show that these two objectives are incompatible, in the sense that as the approximation error of the hypothesis class decreases
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 800 (23 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
Surface Simplification Using Quadric Error Metrics
"... Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplifi ..."
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Cited by 1174 (16 self)
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simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm
Greed is Good: Algorithmic Results for Sparse Approximation
, 2004
"... This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal representa ..."
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Cited by 916 (9 self)
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is an approximation algorithm for the sparse problem over a quasiincoherent dictionary. That is, for every input signal, OMP calculates a sparse approximant whose error is only a small factor worse than the minimal error that can be attained with the same number of terms.
A Guided Tour to Approximate String Matching
 ACM COMPUTING SURVEYS
, 1999
"... We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining t ..."
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Cited by 598 (36 self)
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We survey the current techniques to cope with the problem of string matching allowing errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining
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