• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.69-78
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• 2009

The accuracy of wavelet approximation at resolution h = $2^{-k}$ to a smooth function f is limited by O($h^M$), where M is the number of vanishing moments of the mother wavelet ${\psi}$; that is, the approximation order of wavelet approximation is M - 1. High accuracy points of wavelet approximation are of interest in some applications such as signal processing and numerical approximation. In this paper, we prove the scaling and translating properties of high accuracy points of wavelet approximation. To illustrate the results in this paper, we also present two examples of high accuracy points of wavelet approximation.

• 대한수학회보
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• 제52권1호
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• pp.69-83
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• 2015

In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.

• Kyungpook Mathematical Journal
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• 제57권3호
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.

• Industrial Engineering and Management Systems
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• 제7권2호
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• pp.143-149
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• 2008

There have been some approximation analysis methods for a GI/G/1 queueing system. As one of them, an approximation technique for the steady-state probability in the GI/G/1 queueing system based on the iteration numerical calculation has been proposed. As another one, an approximation formula of the average queue length in the GI/G/1 queueing system by using the diffusion approximation or the heuristics extended diffusion approximation has been developed. In this article, an approximation technique in order to analyze the GI/G/1 queueing system is considered and then the formulae of both the steady-state probability and the average queue length in the GI/G/1 queueing system are proposed. Through some numerical examples by the proposed technique, the existing approximation methods, and the Monte Carlo simulation, the effectiveness of the proposed approximation technique is verified.

• 대한수학회논문집
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• 제9권2호
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• pp.293-298
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• 1994

It is well known that the approximation property and the compact approximation property are not hereditary properties; that is, a closed subspace M of a Banach space X with the (compact) approximation property need not have the (compact) approximation property. In 1973, A. Davie [2] proved that for each 2 < p < $\infty$, there is a closed subspace $Y_{p}$ of $\ell_{p}$ which does not have the approximation property. In fact, the space Davie constructed even fails to have a weaker property, the compact approximation property. In 1991, A. Lima [12] proved that if X is a Banach space with the approximation property and a closed subspace M of X is locally $\lambda$-complemented in X for some $1\leq\lambda < $\infty$, then M has the approximation property.(omitted)

• Communications for Statistical Applications and Methods
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• 제19권2호
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• pp.267-276
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• 2012

Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

• 통합자연과학논문집
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• 제9권1호
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• 응용통계연구
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• 제24권6호
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• pp.1161-1168
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• 2011

The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

• 충청수학회지
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• 제17권1호
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• pp.77-83
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• 2004

The aim of this work is to generalize parametric approximation in order to apply them to an one-sided $L_1$-approximation. A natural question now arises : when is the parameter map $$P:f{\rightarrow}P_{K(f)}(f)$$ continuous on $C_1(X)$ ? We find some results with a monotone decreasing sequence about above question.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제7권1호
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• pp.81-98
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• 2013

Since Probabilistic Latent Semantic Analysis (PLSA) and Latent Dirichlet Allocation (LDA) were introduced, many revised or extended topic models have appeared. Due to the intractable likelihood of these models, training any topic model requires to use some approximation algorithm such as variational approximation, Laplace approximation, or Markov chain Monte Carlo (MCMC). Although these approximation algorithms perform well, training a topic model is still computationally expensive given the large amount of data it requires. In this paper, we propose a new method, called non-simultaneous sampling deactivation, for efficient approximation of parameters in a topic model. While each random variable is normally sampled or obtained by a single predefined burn-in period in the traditional approximation algorithms, our new method is based on the observation that the random variable nodes in one topic model have all different periods of convergence. During the iterative approximation process, the proposed method allows each random variable node to be terminated or deactivated when it is converged. Therefore, compared to the traditional approximation ways in which usually every node is deactivated concurrently, the proposed method achieves the inference efficiency in terms of time and memory. We do not propose a new approximation algorithm, but a new process applicable to the existing approximation algorithms. Through experiments, we show the time and memory efficiency of the method, and discuss about the tradeoff between the efficiency of the approximation process and the parameter consistency.